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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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F(x)=e^{-x\u002F\\theta},\\qquad 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memoryless property,",[1797,2542,2544],{"className":2543},[1942],[1797,2545,2547,2604],{"className":2546},[1800],[1797,2548,2550],{"className":2549},[1804],[1806,2551,2552],{"xmlns":1808,"display":1951},[1810,2553,2554,2601],{},[1813,2555,2556,2559,2561,2563,2565,2568,2571,2574,2577,2579,2581,2583,2585,2587,2589,2591,2593,2595,2597,2599],{},[1816,2557,2558],{},"P",[1820,2560,1962],{"stretchy":1961},[1816,2562,1818],{},[1820,2564,1900],{},[1816,2566,2567],{},"s",[1820,2569,2570],{},"+",[1816,2572,2573],{},"t",[1820,2575,2576],{},"∣",[1816,2578,1818],{},[1820,2580,1900],{},[1816,2582,2567],{},[1820,2584,1968],{"stretchy":1961},[1820,2586,1971],{},[1816,2588,2558],{},[1820,2590,1962],{"stretchy":1961},[1816,2592,1818],{},[1820,2594,1900],{},[1816,2596,2573],{},[1820,2598,1968],{"stretchy":1961},[1820,2600,1938],{"separator":1836},[1828,2602,2603],{"encoding":1830},"P(X>s+t\\mid X>s)=P(X>t),",[1797,2605,2607,2631,2652,2670,2689,2710,2734],{"className":2606,"ariaHidden":1836},[1835],[1797,2608,2610,2613,2616,2619,2622,2625,2628],{"className":2609},[1840],[1797,2611],{"className":2612,"style":2058},[1844],[1797,2614,2558],{"className":2615,"style":2252},[1849,1850],[1797,2617,1962],{"className":2618},[2066],[1797,2620,1818],{"className":2621,"style":1851},[1849,1850],[1797,2623],{"className":2624,"style":1856},[1855],[1797,2626,1900],{"className":2627},[1860],[1797,2629],{"className":2630,"style":1856},[1855],[1797,2632,2634,2638,2641,2645,2649],{"className":2633},[1840],[1797,2635],{"className":2636,"style":2637},[1844],"height:0.6667em;vertical-align:-0.0833em;",[1797,2639,2567],{"className":2640},[1849,1850],[1797,2642],{"className":2643,"style":2644},[1855],"margin-right:0.2222em;",[1797,2646,2570],{"className":2647},[2648],"mbin",[1797,2650],{"className":2651,"style":2644},[1855],[1797,2653,2655,2658,2661,2664,2667],{"className":2654},[1840],[1797,2656],{"className":2657,"style":2058},[1844],[1797,2659,2573],{"className":2660},[1849,1850],[1797,2662],{"className":2663,"style":1856},[1855],[1797,2665,2576],{"className":2666},[1860],[1797,2668],{"className":2669,"style":1856},[1855],[1797,2671,2673,2677,2680,2683,2686],{"className":2672},[1840],[1797,2674],{"className":2675,"style":2676},[1844],"height:0.7224em;vertical-align:-0.0391em;",[1797,2678,1818],{"className":2679,"style":1851},[1849,1850],[1797,2681],{"className":2682,"style":1856},[1855],[1797,2684,1900],{"className":2685},[1860],[1797,2687],{"className":2688,"style":1856},[1855],[1797,2690,2692,2695,2698,2701,2704,2707],{"className":2691},[1840],[1797,2693],{"className":2694,"style":2058},[1844],[1797,2696,2567],{"className":2697},[1849,1850],[1797,2699,1968],{"className":2700},[2073],[1797,2702],{"className":2703,"style":1856},[1855],[1797,2705,1971],{"className":2706},[1860],[1797,2708],{"className":2709,"style":1856},[1855],[1797,2711,2713,2716,2719,2722,2725,2728,2731],{"className":2712},[1840],[1797,2714],{"className":2715,"style":2058},[1844],[1797,2717,2558],{"className":2718,"style":2252},[1849,1850],[1797,2720,1962],{"className":2721},[2066],[1797,2723,1818],{"className":2724,"style":1851},[1849,1850],[1797,2726],{"className":2727,"style":1856},[1855],[1797,2729,1900],{"className":2730},[1860],[1797,2732],{"className":2733,"style":1856},[1855],[1797,2735,2737,2740,2743,2746],{"className":2736},[1840],[1797,2738],{"className":2739,"style":2058},[1844],[1797,2741,2573],{"className":2742},[1849,1850],[1797,2744,1968],{"className":2745},[2073],[1797,2747,1938],{"className":2748},[2220],[1793,2750,2751],{},"is convenient but often unrealistic: exceeding a large threshold supplies no information about further excess. Use Exponential as a benchmark, not a default.",[1876,2753,2755],{"id":2754},"_2-gamma-flexible-centre-with-exponential-type-tail","2. Gamma: flexible centre with exponential-type tail",[1793,2757,2758,2759,2812,2813,1938],{},"With shape ",[1797,2760,2762,2781],{"className":2761},[1800],[1797,2763,2765],{"className":2764},[1804],[1806,2766,2767],{"xmlns":1808},[1810,2768,2769,2778],{},[1813,2770,2771,2774,2776],{},[1816,2772,2773],{},"k",[1820,2775,1900],{},[1824,2777,1826],{},[1828,2779,2780],{"encoding":1830},"k>0",[1797,2782,2784,2803],{"className":2783,"ariaHidden":1836},[1835],[1797,2785,2787,2790,2794,2797,2800],{"className":2786},[1840],[1797,2788],{"className":2789,"style":1915},[1844],[1797,2791,2773],{"className":2792,"style":2793},[1849,1850],"margin-right:0.0315em;",[1797,2795],{"className":2796,"style":1856},[1855],[1797,2798,1900],{"className":2799},[1860],[1797,2801],{"className":2802,"style":1856},[1855],[1797,2804,2806,2809],{"className":2805},[1840],[1797,2807],{"className":2808,"style":1870},[1844],[1797,2810,1826],{"className":2811},[1849]," and scale 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The lognormal tail is heavier than Gamma or Exponential but lighter than a power-law Pareto tail.",[1876,4318,4320],{"id":4319},"_4-same-mean-different-decision","4. Same mean, different decision",[1793,4322,4323],{},"Choose parameters so all three models have mean £5,000:",[4325,4326,4327,4347],"table",{},[4328,4329,4330],"thead",{},[4331,4332,4333,4337,4340,4344],"tr",{},[4334,4335,4336],"th",{},"Model",[4334,4338,4339],{},"Parameters",[4334,4341,4343],{"align":4342},"right","SD",[4334,4345,4346],{"align":4342},"99% quantile",[4348,4349,4350,4428,4545],"tbody",{},[4331,4351,4352,4356,4422,4425],{},[4353,4354,4355],"td",{},"Exponential",[4353,4357,4358],{},[1797,4359,4361,4380],{"className":4360},[1800],[1797,4362,4364],{"className":4363},[1804],[1806,4365,4366],{"xmlns":1808},[1810,4367,4368,4377],{},[1813,4369,4370,4372,4374],{},[1816,4371,1897],{},[1820,4373,1971],{},[1824,4375,4376],{},"5,000",[1828,4378,4379],{"encoding":1830},"\\theta=5{,}000",[1797,4381,4383,4401],{"className":4382,"ariaHidden":1836},[1835],[1797,4384,4386,4389,4392,4395,4398],{"className":4385},[1840],[1797,4387],{"className":4388,"style":3354},[1844],[1797,4390,1897],{"className":4391,"style":1919},[1849,1850],[1797,4393],{"className":4394,"style":1856},[1855],[1797,4396,1971],{"className":4397},[1860],[1797,4399],{"className":4400,"style":1856},[1855],[1797,4402,4404,4408,4412,4418],{"className":4403},[1840],[1797,4405],{"className":4406,"style":4407},[1844],"height:0.8389em;vertical-align:-0.1944em;",[1797,4409,4411],{"className":4410},[1849],"5",[1797,4413,4415],{"className":4414},[1849],[1797,4416,1938],{"className":4417},[2220],[1797,4419,4421],{"className":4420},[1849],"000",[4353,4423,4424],{"align":4342},"£5,000",[4353,4426,4427],{"align":4342},"£23,026",[4331,4429,4430,4433,4539,4542],{},[4353,4431,4432],{},"Gamma",[4353,4434,4435],{},[1797,4436,4438,4469],{"className":4437},[1800],[1797,4439,4441],{"className":4440},[1804],[1806,4442,4443],{"xmlns":1808},[1810,4444,4445,4466],{},[1813,4446,4447,4449,4451,4454,4456,4459,4461,4463],{},[1816,4448,2773],{},[1820,4450,1971],{},[1824,4452,4453],{},"4",[1820,4455,1938],{"separator":1836},[4150,4457,4458],{}," ",[1816,4460,1897],{},[1820,4462,1971],{},[1824,4464,4465],{},"1,250",[1828,4467,4468],{"encoding":1830},"k=4,\\ \\theta=1{,}250",[1797,4470,4472,4490,4520],{"className":4471,"ariaHidden":1836},[1835],[1797,4473,4475,4478,4481,4484,4487],{"className":4474},[1840],[1797,4476],{"className":4477,"style":3354},[1844],[1797,4479,2773],{"className":4480,"style":2793},[1849,1850],[1797,4482],{"className":4483,"style":1856},[1855],[1797,4485,1971],{"className":4486},[1860],[1797,4488],{"className":4489,"style":1856},[1855],[1797,4491,4493,4496,4499,4502,4505,4508,4511,4514,4517],{"className":4492},[1840],[1797,4494],{"className":4495,"style":3599},[1844],[1797,4497,4453],{"className":4498},[1849],[1797,4500,1938],{"className":4501},[2220],[1797,4503,4458],{"className":4504},[1855],[1797,4506],{"className":4507,"style":2228},[1855],[1797,4509,1897],{"className":4510,"style":1919},[1849,1850],[1797,4512],{"className":4513,"style":1856},[1855],[1797,4515,1971],{"className":4516},[1860],[1797,4518],{"className":4519,"style":1856},[1855],[1797,4521,4523,4526,4529,4535],{"className":4522},[1840],[1797,4524],{"className":4525,"style":4407},[1844],[1797,4527,1977],{"className":4528},[1849],[1797,4530,4532],{"className":4531},[1849],[1797,4533,1938],{"className":4534},[2220],[1797,4536,4538],{"className":4537},[1849],"250",[4353,4540,4541],{"align":4342},"£2,500",[4353,4543,4544],{"align":4342},"£12,556",[4331,4546,4547,4550,4693,4696],{},[4353,4548,4549],{},"Lognormal",[4353,4551,4552,4553,4598,4599],{},"CV ",[1797,4554,4556,4573],{"className":4555},[1800],[1797,4557,4559],{"className":4558},[1804],[1806,4560,4561],{"xmlns":1808},[1810,4562,4563,4570],{},[1813,4564,4565,4567],{},[1820,4566,1971],{},[1824,4568,4569],{},"1.5",[1828,4571,4572],{"encoding":1830},"=1.5",[1797,4574,4576,4589],{"className":4575,"ariaHidden":1836},[1835],[1797,4577,4579,4583,4586],{"className":4578},[1840],[1797,4580],{"className":4581,"style":4582},[1844],"height:0.3669em;",[1797,4584,1971],{"className":4585},[1860],[1797,4587],{"className":4588,"style":1856},[1855],[1797,4590,4592,4595],{"className":4591},[1840],[1797,4593],{"className":4594,"style":1870},[1844],[1797,4596,4569],{"className":4597},[1849],"; ",[1797,4600,4602,4632],{"className":4601},[1800],[1797,4603,4605],{"className":4604},[1804],[1806,4606,4607],{"xmlns":1808},[1810,4608,4609,4629],{},[1813,4610,4611,4613,4615,4618,4620,4622,4624,4626],{},[1816,4612,3575],{},[1820,4614,1971],{},[1824,4616,4617],{},"7.9279",[1820,4619,1938],{"separator":1836},[4150,4621,4458],{},[1816,4623,3582],{},[1820,4625,1971],{},[1824,4627,4628],{},"1.0857",[1828,4630,4631],{"encoding":1830},"\\mu=7.9279,\\ \\sigma=1.0857",[1797,4633,4635,4654,4684],{"className":4634,"ariaHidden":1836},[1835],[1797,4636,4638,4642,4645,4648,4651],{"className":4637},[1840],[1797,4639],{"className":4640,"style":4641},[1844],"height:0.625em;vertical-align:-0.1944em;",[1797,4643,3575],{"className":4644},[1849,1850],[1797,4646],{"className":4647,"style":1856},[1855],[1797,4649,1971],{"className":4650},[1860],[1797,4652],{"className":4653,"style":1856},[1855],[1797,4655,4657,4660,4663,4666,4669,4672,4675,4678,4681],{"className":4656},[1840],[1797,4658],{"className":4659,"style":4407},[1844],[1797,4661,4617],{"className":4662},[1849],[1797,4664,1938],{"className":4665},[2220],[1797,4667,4458],{"className":4668},[1855],[1797,4670],{"className":4671,"style":2228},[1855],[1797,4673,3582],{"className":4674,"style":3652},[1849,1850],[1797,4676],{"className":4677,"style":1856},[1855],[1797,4679,1971],{"className":4680},[1860],[1797,4682],{"className":4683,"style":1856},[1855],[1797,4685,4687,4690],{"className":4686},[1840],[1797,4688],{"className":4689,"style":1870},[1844],[1797,4691,4628],{"className":4692},[1849],[4353,4694,4695],{"align":4342},"£7,500",[4353,4697,4698],{"align":4342},"about £34,665",[1793,4700,4701],{},"An expected-loss calculation sees no difference. A capital or reinsurance decision does.",[4703,4704],"pyodide",{"code64":4705,"layout":4706,"locale":7,"packages":4707,"title":4708},"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","vertical","numpy,scipy,matplotlib","Equal means, unequal tails",[1876,4710,4712],{"id":4711},"_5-contracts-transform-severity","5. Contracts transform severity",[4714,4715,4717],"h3",{"id":4716},"ordinary-deductible","Ordinary deductible",[1793,4719,4720,4721,4750],{},"With deductible ",[1797,4722,4724,4738],{"className":4723},[1800],[1797,4725,4727],{"className":4726},[1804],[1806,4728,4729],{"xmlns":1808},[1810,4730,4731,4736],{},[1813,4732,4733],{},[1816,4734,4735],{},"d",[1828,4737,4735],{"encoding":1830},[1797,4739,4741],{"className":4740,"ariaHidden":1836},[1835],[1797,4742,4744,4747],{"className":4743},[1840],[1797,4745],{"className":4746,"style":3354},[1844],[1797,4748,4735],{"className":4749},[1849,1850],", insurer payment per loss is",[1797,4752,4754],{"className":4753},[1942],[1797,4755,4757,4791],{"className":4756},[1800],[1797,4758,4760],{"className":4759},[1804],[1806,4761,4762],{"xmlns":1808,"display":1951},[1810,4763,4764,4788],{},[1813,4765,4766,4769,4771,4773,4775,4777,4779,4786],{},[1816,4767,4768],{},"Y",[1820,4770,1971],{},[1820,4772,1962],{"stretchy":1961},[1816,4774,1818],{},[1820,4776,1990],{},[1816,4778,4735],{},[4780,4781,4782,4784],"msub",{},[1820,4783,1968],{"stretchy":1961},[1820,4785,2570],{},[1816,4787,2420],{"mathvariant":1995},[1828,4789,4790],{"encoding":1830},"Y=(X-d)_+.",[1797,4792,4794,4813,4834],{"className":4793,"ariaHidden":1836},[1835],[1797,4795,4797,4801,4804,4807,4810],{"className":4796},[1840],[1797,4798],{"className":4799,"style":4800},[1844],"height:0.6833em;",[1797,4802,4768],{"className":4803,"style":2644},[1849,1850],[1797,4805],{"className":4806,"style":1856},[1855],[1797,4808,1971],{"className":4809},[1860],[1797,4811],{"className":4812,"style":1856},[1855],[1797,4814,4816,4819,4822,4825,4828,4831],{"className":4815},[1840],[1797,4817],{"className":4818,"style":2058},[1844],[1797,4820,1962],{"className":4821},[2066],[1797,4823,1818],{"className":4824,"style":1851},[1849,1850],[1797,4826],{"className":4827,"style":2644},[1855],[1797,4829,1990],{"className":4830},[2648],[1797,4832],{"className":4833,"style":2644},[1855],[1797,4835,4837,4840,4843,4886],{"className":4836},[1840],[1797,4838],{"className":4839,"style":2058},[1844],[1797,4841,4735],{"className":4842},[1849,1850],[1797,4844,4846,4849],{"className":4845},[2073],[1797,4847,1968],{"className":4848},[2073],[1797,4850,4852],{"className":4851},[2177],[1797,4853,4855,4877],{"className":4854},[2103,2104],[1797,4856,4858,4874],{"className":4857},[2108],[1797,4859,4862],{"className":4860,"style":4861},[2112],"height:0.2583em;",[1797,4863,4865,4868],{"style":4864},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1797,4866],{"className":4867,"style":2194},[2120],[1797,4869,4871],{"className":4870},[2198,2199,2200,2201],[1797,4872,2570],{"className":4873},[2648,2201],[1797,4875,2155],{"className":4876},[2154],[1797,4878,4880],{"className":4879},[2108],[1797,4881,4884],{"className":4882,"style":4883},[2112],"height:0.2083em;",[1797,4885],{},[1797,4887,2420],{"className":4888},[1849],[1793,4890,4891],{},"Unconditional expected payment is",[1797,4893,4895],{"className":4894},[1942],[1797,4896,4898,4978],{"className":4897},[1800],[1797,4899,4901],{"className":4900},[1804],[1806,4902,4903],{"xmlns":1808,"display":1951},[1810,4904,4905,4975],{},[1813,4906,4907,4909,4911,4913,4915,4917,4919,4921,4923,4925,4927,4929,4935,4937,4939,4950,4960,4962,4964,4966,4969,4971,4973],{},[1816,4908,2380],{},[1820,4910,2383],{"stretchy":1961},[1816,4912,4768],{},[1820,4914,2388],{"stretchy":1961},[1820,4916,1971],{},[1816,4918,2380],{},[1820,4920,2383],{"stretchy":1961},[1820,4922,1962],{"stretchy":1961},[1816,4924,1818],{},[1820,4926,1990],{},[1816,4928,4735],{},[4780,4930,4931,4933],{},[1820,4932,1968],{"stretchy":1961},[1820,4934,2570],{},[1820,4936,2388],{"stretchy":1961},[1820,4938,1971],{},[4940,4941,4942,4945,4947],"msubsup",{},[1820,4943,4944],{},"∫",[1816,4946,4735],{},[1816,4948,4949],{"mathvariant":1995},"∞",[4780,4951,4952,4958],{},[2005,4953,4954,4956],{"accent":1836},[1816,4955,2009],{},[1820,4957,2012],{},[1816,4959,1818],{},[1820,4961,1962],{"stretchy":1961},[1816,4963,1965],{},[1820,4965,1968],{"stretchy":1961},[4150,4967,4968],{}," ",[1816,4970,4735],{},[1816,4972,1965],{},[1816,4974,2420],{"mathvariant":1995},[1828,4976,4977],{"encoding":1830},"E[Y]=E[(X-d)_+]=\\int_d^\\infty\\bar F_X(x)\\,dx.",[1797,4979,4981,5008,5033,5094],{"className":4980,"ariaHidden":1836},[1835],[1797,4982,4984,4987,4990,4993,4996,4999,5002,5005],{"className":4983},[1840],[1797,4985],{"className":4986,"style":2058},[1844],[1797,4988,2380],{"className":4989,"style":2436},[1849,1850],[1797,4991,2383],{"className":4992},[2066],[1797,4994,4768],{"className":4995,"style":2644},[1849,1850],[1797,4997,2388],{"className":4998},[2073],[1797,5000],{"className":5001,"style":1856},[1855],[1797,5003,1971],{"className":5004},[1860],[1797,5006],{"className":5007,"style":1856},[1855],[1797,5009,5011,5014,5017,5021,5024,5027,5030],{"className":5010},[1840],[1797,5012],{"className":5013,"style":2058},[1844],[1797,5015,2380],{"className":5016,"style":2436},[1849,1850],[1797,5018,5020],{"className":5019},[2066],"[(",[1797,5022,1818],{"className":5023,"style":1851},[1849,1850],[1797,5025],{"className":5026,"style":2644},[1855],[1797,5028,1990],{"className":5029},[2648],[1797,5031],{"className":5032,"style":2644},[1855],[1797,5034,5036,5039,5042,5082,5085,5088,5091],{"className":5035},[1840],[1797,5037],{"className":5038,"style":2058},[1844],[1797,5040,4735],{"className":5041},[1849,1850],[1797,5043,5045,5048],{"className":5044},[2073],[1797,5046,1968],{"className":5047},[2073],[1797,5049,5051],{"className":5050},[2177],[1797,5052,5054,5074],{"className":5053},[2103,2104],[1797,5055,5057,5071],{"className":5056},[2108],[1797,5058,5060],{"className":5059,"style":4861},[2112],[1797,5061,5062,5065],{"style":4864},[1797,5063],{"className":5064,"style":2194},[2120],[1797,5066,5068],{"className":5067},[2198,2199,2200,2201],[1797,5069,2570],{"className":5070},[2648,2201],[1797,5072,2155],{"className":5073},[2154],[1797,5075,5077],{"className":5076},[2108],[1797,5078,5080],{"className":5079,"style":4883},[2112],[1797,5081],{},[1797,5083,2388],{"className":5084},[2073],[1797,5086],{"className":5087,"style":1856},[1855],[1797,5089,1971],{"className":5090},[1860],[1797,5092],{"className":5093,"style":1856},[1855],[1797,5095,5097,5101,5159,5162,5233,5236,5239,5242,5245,5248,5251],{"className":5096},[1840],[1797,5098],{"className":5099,"style":5100},[1844],"height:2.3262em;vertical-align:-0.9119em;",[1797,5102,5104,5110],{"className":5103},[2476],[1797,5105,4944],{"className":5106,"style":5109},[2476,5107,5108],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[1797,5111,5113],{"className":5112},[2177],[1797,5114,5116,5150],{"className":5115},[2103,2104],[1797,5117,5119,5147],{"className":5118},[2108],[1797,5120,5123,5135],{"className":5121,"style":5122},[2112],"height:1.4143em;",[1797,5124,5126,5129],{"style":5125},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[1797,5127],{"className":5128,"style":2194},[2120],[1797,5130,5132],{"className":5131},[2198,2199,2200,2201],[1797,5133,4735],{"className":5134},[1849,1850,2201],[1797,5136,5138,5141],{"style":5137},"top:-3.8129em;margin-right:0.05em;",[1797,5139],{"className":5140,"style":2194},[2120],[1797,5142,5144],{"className":5143},[2198,2199,2200,2201],[1797,5145,4949],{"className":5146},[1849,2201],[1797,5148,2155],{"className":5149},[2154],[1797,5151,5153],{"className":5152},[2108],[1797,5154,5157],{"className":5155,"style":5156},[2112],"height:0.9119em;",[1797,5158],{},[1797,5160],{"className":5161,"style":2228},[1855],[1797,5163,5165,5196],{"className":5164},[1849],[1797,5166,5168],{"className":5167},[1849,2232],[1797,5169,5171],{"className":5170},[2103],[1797,5172,5174],{"className":5173},[2108],[1797,5175,5177,5185],{"className":5176,"style":2242},[2112],[1797,5178,5179,5182],{"style":2245},[1797,5180],{"className":5181,"style":2121},[2120],[1797,5183,2009],{"className":5184,"style":2252},[1849,1850],[1797,5186,5187,5190],{"style":2255},[1797,5188],{"className":5189,"style":2121},[2120],[1797,5191,5193],{"className":5192,"style":2263},[2262],[1797,5194,2012],{"className":5195},[1849],[1797,5197,5199],{"className":5198},[2177],[1797,5200,5202,5224],{"className":5201},[2103,2104],[1797,5203,5205,5221],{"className":5204},[2108],[1797,5206,5209],{"className":5207,"style":5208},[2112],"height:0.3283em;",[1797,5210,5212,5215],{"style":5211},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1797,5213],{"className":5214,"style":2194},[2120],[1797,5216,5218],{"className":5217},[2198,2199,2200,2201],[1797,5219,1818],{"className":5220,"style":1851},[1849,1850,2201],[1797,5222,2155],{"className":5223},[2154],[1797,5225,5227],{"className":5226},[2108],[1797,5228,5231],{"className":5229,"style":5230},[2112],"height:0.15em;",[1797,5232],{},[1797,5234,1962],{"className":5235},[2066],[1797,5237,1965],{"className":5238},[1849,1850],[1797,5240,1968],{"className":5241},[2073],[1797,5243],{"className":5244,"style":2228},[1855],[1797,5246,4735],{"className":5247},[1849,1850],[1797,5249,1965],{"className":5250},[1849,1850],[1797,5252,2420],{"className":5253},[1849],[1793,5255,5256,5257,5285,5286,1938],{},"For Exponential ",[1797,5258,5260,5273],{"className":5259},[1800],[1797,5261,5263],{"className":5262},[1804],[1806,5264,5265],{"xmlns":1808},[1810,5266,5267,5271],{},[1813,5268,5269],{},[1816,5270,1818],{},[1828,5272,1818],{"encoding":1830},[1797,5274,5276],{"className":5275,"ariaHidden":1836},[1835],[1797,5277,5279,5282],{"className":5278},[1840],[1797,5280],{"className":5281,"style":4800},[1844],[1797,5283,1818],{"className":5284,"style":1851},[1849,1850]," with mean ",[1797,5287,5289,5303],{"className":5288},[1800],[1797,5290,5292],{"className":5291},[1804],[1806,5293,5294],{"xmlns":1808},[1810,5295,5296,5300],{},[1813,5297,5298],{},[1816,5299,1897],{},[1828,5301,5302],{"encoding":1830},"\\theta",[1797,5304,5306],{"className":5305,"ariaHidden":1836},[1835],[1797,5307,5309,5312],{"className":5308},[1840],[1797,5310],{"className":5311,"style":3354},[1844],[1797,5313,1897],{"className":5314,"style":1919},[1849,1850],[1797,5316,5318],{"className":5317},[1942],[1797,5319,5321,5373],{"className":5320},[1800],[1797,5322,5324],{"className":5323},[1804],[1806,5325,5326],{"xmlns":1808,"display":1951},[1810,5327,5328,5370],{},[1813,5329,5330,5332,5334,5336,5338,5340,5342,5348,5350,5352,5354,5368],{},[1816,5331,2380],{},[1820,5333,2383],{"stretchy":1961},[1820,5335,1962],{"stretchy":1961},[1816,5337,1818],{},[1820,5339,1990],{},[1816,5341,4735],{},[4780,5343,5344,5346],{},[1820,5345,1968],{"stretchy":1961},[1820,5347,2570],{},[1820,5349,2388],{"stretchy":1961},[1820,5351,1971],{},[1816,5353,1897],{},[1981,5355,5356,5358],{},[1816,5357,1985],{},[1813,5359,5360,5362,5364,5366],{},[1820,5361,1990],{},[1816,5363,4735],{},[1816,5365,1996],{"mathvariant":1995},[1816,5367,1897],{},[1816,5369,2420],{"mathvariant":1995},[1828,5371,5372],{"encoding":1830},"E[(X-d)_+]=\\theta e^{-d\u002F\\theta}.",[1797,5374,5376,5400,5461],{"className":5375,"ariaHidden":1836},[1835],[1797,5377,5379,5382,5385,5388,5391,5394,5397],{"className":5378},[1840],[1797,5380],{"className":5381,"style":2058},[1844],[1797,5383,2380],{"className":5384,"style":2436},[1849,1850],[1797,5386,5020],{"className":5387},[2066],[1797,5389,1818],{"className":5390,"style":1851},[1849,1850],[1797,5392],{"className":5393,"style":2644},[1855],[1797,5395,1990],{"className":5396},[2648],[1797,5398],{"className":5399,"style":2644},[1855],[1797,5401,5403,5406,5409,5449,5452,5455,5458],{"className":5402},[1840],[1797,5404],{"className":5405,"style":2058},[1844],[1797,5407,4735],{"className":5408},[1849,1850],[1797,5410,5412,5415],{"className":5411},[2073],[1797,5413,1968],{"className":5414},[2073],[1797,5416,5418],{"className":5417},[2177],[1797,5419,5421,5441],{"className":5420},[2103,2104],[1797,5422,5424,5438],{"className":5423},[2108],[1797,5425,5427],{"className":5426,"style":4861},[2112],[1797,5428,5429,5432],{"style":4864},[1797,5430],{"className":5431,"style":2194},[2120],[1797,5433,5435],{"className":5434},[2198,2199,2200,2201],[1797,5436,2570],{"className":5437},[2648,2201],[1797,5439,2155],{"className":5440},[2154],[1797,5442,5444],{"className":5443},[2108],[1797,5445,5447],{"className":5446,"style":4883},[2112],[1797,5448],{},[1797,5450,2388],{"className":5451},[2073],[1797,5453],{"className":5454,"style":1856},[1855],[1797,5456,1971],{"className":5457},[1860],[1797,5459],{"className":5460,"style":1856},[1855],[1797,5462,5464,5467,5470,5511],{"className":5463},[1840],[1797,5465],{"className":5466,"style":2187},[1844],[1797,5468,1897],{"className":5469,"style":1919},[1849,1850],[1797,5471,5473,5476],{"className":5472},[1849],[1797,5474,1985],{"className":5475},[1849,1850],[1797,5477,5479],{"className":5478},[2177],[1797,5480,5482],{"className":5481},[2103],[1797,5483,5485],{"className":5484},[2108],[1797,5486,5488],{"className":5487,"style":2187},[2112],[1797,5489,5490,5493],{"style":2190},[1797,5491],{"className":5492,"style":2194},[2120],[1797,5494,5496],{"className":5495},[2198,2199,2200,2201],[1797,5497,5499,5502,5505,5508],{"className":5498},[1849,2201],[1797,5500,1990],{"className":5501},[1849,2201],[1797,5503,4735],{"className":5504},[1849,1850,2201],[1797,5506,1996],{"className":5507},[1849,2201],[1797,5509,1897],{"className":5510,"style":1919},[1849,1850,2201],[1797,5512,2420],{"className":5513},[1849],[1793,5515,5516,5517,5581,5582,5646,5647,2420],{},"At ",[1797,5518,5520,5541],{"className":5519},[1800],[1797,5521,5523],{"className":5522},[1804],[1806,5524,5525],{"xmlns":1808},[1810,5526,5527,5538],{},[1813,5528,5529,5531,5533,5536],{},[1816,5530,1897],{},[1820,5532,1971],{},[1816,5534,5535],{"mathvariant":1995},"£",[1824,5537,4376],{},[1828,5539,5540],{"encoding":1830},"\\theta=£5{,}000",[1797,5542,5544,5562],{"className":5543,"ariaHidden":1836},[1835],[1797,5545,5547,5550,5553,5556,5559],{"className":5546},[1840],[1797,5548],{"className":5549,"style":3354},[1844],[1797,5551,1897],{"className":5552,"style":1919},[1849,1850],[1797,5554],{"className":5555,"style":1856},[1855],[1797,5557,1971],{"className":5558},[1860],[1797,5560],{"className":5561,"style":1856},[1855],[1797,5563,5565,5568,5572,5578],{"className":5564},[1840],[1797,5566],{"className":5567,"style":3599},[1844],[1797,5569,5571],{"className":5570},[1849],"£5",[1797,5573,5575],{"className":5574},[1849],[1797,5576,1938],{"className":5577},[2220],[1797,5579,4421],{"className":5580},[1849]," and ",[1797,5583,5585,5606],{"className":5584},[1800],[1797,5586,5588],{"className":5587},[1804],[1806,5589,5590],{"xmlns":1808},[1810,5591,5592,5603],{},[1813,5593,5594,5596,5598,5600],{},[1816,5595,4735],{},[1820,5597,1971],{},[1816,5599,5535],{"mathvariant":1995},[1824,5601,5602],{},"2,000",[1828,5604,5605],{"encoding":1830},"d=£2{,}000",[1797,5607,5609,5627],{"className":5608,"ariaHidden":1836},[1835],[1797,5610,5612,5615,5618,5621,5624],{"className":5611},[1840],[1797,5613],{"className":5614,"style":3354},[1844],[1797,5616,4735],{"className":5617},[1849,1850],[1797,5619],{"className":5620,"style":1856},[1855],[1797,5622,1971],{"className":5623},[1860],[1797,5625],{"className":5626,"style":1856},[1855],[1797,5628,5630,5633,5637,5643],{"className":5629},[1840],[1797,5631],{"className":5632,"style":3599},[1844],[1797,5634,5636],{"className":5635},[1849],"£2",[1797,5638,5640],{"className":5639},[1849],[1797,5641,1938],{"className":5642},[2220],[1797,5644,4421],{"className":5645},[1849],", expected insurer payment per underlying loss is ",[1797,5648,5650,5683],{"className":5649},[1800],[1797,5651,5653],{"className":5652},[1804],[1806,5654,5655],{"xmlns":1808},[1810,5656,5657,5680],{},[1813,5658,5659,5661,5672,5675,5677],{},[1824,5660,4376],{},[1981,5662,5663,5665],{},[1816,5664,1985],{},[1813,5666,5667,5669],{},[1820,5668,1990],{},[1824,5670,5671],{},"0.4",[1820,5673,5674],{},"≈",[1816,5676,5535],{"mathvariant":1995},[1824,5678,5679],{},"3,352",[1828,5681,5682],{"encoding":1830},"5{,}000e^{-0.4}\\approx£3{,}352",[1797,5684,5686,5749],{"className":5685,"ariaHidden":1836},[1835],[1797,5687,5689,5693,5696,5702,5705,5740,5743,5746],{"className":5688},[1840],[1797,5690],{"className":5691,"style":5692},[1844],"height:1.0085em;vertical-align:-0.1944em;",[1797,5694,4411],{"className":5695},[1849],[1797,5697,5699],{"className":5698},[1849],[1797,5700,1938],{"className":5701},[2220],[1797,5703,4421],{"className":5704},[1849],[1797,5706,5708,5711],{"className":5707},[1849],[1797,5709,1985],{"className":5710},[1849,1850],[1797,5712,5714],{"className":5713},[2177],[1797,5715,5717],{"className":5716},[2103],[1797,5718,5720],{"className":5719},[2108],[1797,5721,5723],{"className":5722,"style":3665},[2112],[1797,5724,5725,5728],{"style":3126},[1797,5726],{"className":5727,"style":2194},[2120],[1797,5729,5731],{"className":5730},[2198,2199,2200,2201],[1797,5732,5734,5737],{"className":5733},[1849,2201],[1797,5735,1990],{"className":5736},[1849,2201],[1797,5738,5671],{"className":5739},[1849,2201],[1797,5741],{"className":5742,"style":1856},[1855],[1797,5744,5674],{"className":5745},[1860],[1797,5747],{"className":5748,"style":1856},[1855],[1797,5750,5752,5755,5759,5765],{"className":5751},[1840],[1797,5753],{"className":5754,"style":3599},[1844],[1797,5756,5758],{"className":5757},[1849],"£3",[1797,5760,5762],{"className":5761},[1849],[1797,5763,1938],{"className":5764},[2220],[1797,5766,5768],{"className":5767},[1849],"352",[4714,5770,5772],{"id":5771},"limit","Limit",[1793,5774,5775,5776,5806],{},"With payment limit ",[1797,5777,5779,5793],{"className":5778},[1800],[1797,5780,5782],{"className":5781},[1804],[1806,5783,5784],{"xmlns":1808},[1810,5785,5786,5791],{},[1813,5787,5788],{},[1816,5789,5790],{},"u",[1828,5792,5790],{"encoding":1830},[1797,5794,5796],{"className":5795,"ariaHidden":1836},[1835],[1797,5797,5799,5803],{"className":5798},[1840],[1797,5800],{"className":5801,"style":5802},[1844],"height:0.4306em;",[1797,5804,5790],{"className":5805},[1849,1850]," applied to the post-deductible amount,",[1797,5808,5810],{"className":5809},[1942],[1797,5811,5813,5860],{"className":5812},[1800],[1797,5814,5816],{"className":5815},[1804],[1806,5817,5818],{"xmlns":1808,"display":1951},[1810,5819,5820,5857],{},[1813,5821,5822,5824,5826,5829,5831,5834,5836,5838,5840,5842,5848,5850,5852,5855],{},[1816,5823,4768],{},[1820,5825,1971],{},[1816,5827,5828],{},"min",[1820,5830,2402],{},[1820,5832,5833],{"stretchy":1961},"{",[1820,5835,1962],{"stretchy":1961},[1816,5837,1818],{},[1820,5839,1990],{},[1816,5841,4735],{},[4780,5843,5844,5846],{},[1820,5845,1968],{"stretchy":1961},[1820,5847,2570],{},[1820,5849,1938],{"separator":1836},[1816,5851,5790],{},[1820,5853,5854],{"stretchy":1961},"}",[1816,5856,2420],{"mathvariant":1995},[1828,5858,5859],{"encoding":1830},"Y=\\min\\{(X-d)_+,u\\}.",[1797,5861,5863,5881,5906],{"className":5862,"ariaHidden":1836},[1835],[1797,5864,5866,5869,5872,5875,5878],{"className":5865},[1840],[1797,5867],{"className":5868,"style":4800},[1844],[1797,5870,4768],{"className":5871,"style":2644},[1849,1850],[1797,5873],{"className":5874,"style":1856},[1855],[1797,5876,1971],{"className":5877},[1860],[1797,5879],{"className":5880,"style":1856},[1855],[1797,5882,5884,5887,5890,5894,5897,5900,5903],{"className":5883},[1840],[1797,5885],{"className":5886,"style":2058},[1844],[1797,5888,5828],{"className":5889},[2476],[1797,5891,5893],{"className":5892},[2066],"{(",[1797,5895,1818],{"className":5896,"style":1851},[1849,1850],[1797,5898],{"className":5899,"style":2644},[1855],[1797,5901,1990],{"className":5902},[2648],[1797,5904],{"className":5905,"style":2644},[1855],[1797,5907,5909,5912,5915,5955,5958,5961,5964,5967],{"className":5908},[1840],[1797,5910],{"className":5911,"style":2058},[1844],[1797,5913,4735],{"className":5914},[1849,1850],[1797,5916,5918,5921],{"className":5917},[2073],[1797,5919,1968],{"className":5920},[2073],[1797,5922,5924],{"className":5923},[2177],[1797,5925,5927,5947],{"className":5926},[2103,2104],[1797,5928,5930,5944],{"className":5929},[2108],[1797,5931,5933],{"className":5932,"style":4861},[2112],[1797,5934,5935,5938],{"style":4864},[1797,5936],{"className":5937,"style":2194},[2120],[1797,5939,5941],{"className":5940},[2198,2199,2200,2201],[1797,5942,2570],{"className":5943},[2648,2201],[1797,5945,2155],{"className":5946},[2154],[1797,5948,5950],{"className":5949},[2108],[1797,5951,5953],{"className":5952,"style":4883},[2112],[1797,5954],{},[1797,5956,1938],{"className":5957},[2220],[1797,5959],{"className":5960,"style":2228},[1855],[1797,5962,5790],{"className":5963},[1849,1850],[1797,5965,5854],{"className":5966},[2073],[1797,5968,2420],{"className":5969},[1849],[1793,5971,5972,5973,6001,6002,6006],{},"Values recorded at ",[1797,5974,5976,5989],{"className":5975},[1800],[1797,5977,5979],{"className":5978},[1804],[1806,5980,5981],{"xmlns":1808},[1810,5982,5983,5987],{},[1813,5984,5985],{},[1816,5986,5790],{},[1828,5988,5790],{"encoding":1830},[1797,5990,5992],{"className":5991,"ariaHidden":1836},[1835],[1797,5993,5995,5998],{"className":5994},[1840],[1797,5996],{"className":5997,"style":5802},[1844],[1797,5999,5790],{"className":6000},[1849,1850]," may be ",[6003,6004,6005],"strong",{},"right-censored",": the true loss exceeded the observable payment. Treating them as exact claims understates the tail.",[4714,6008,6010],{"id":6009},"conditional-payment-severity","Conditional payment severity",[1793,6012,6013,6014,6017],{},"The mean payment ",[6003,6015,6016],{},"given that a payment occurs"," is",[1797,6019,6021],{"className":6020},[1942],[1797,6022,6024,6098],{"className":6023},[1800],[1797,6025,6027],{"className":6026},[1804],[1806,6028,6029],{"xmlns":1808,"display":1951},[1810,6030,6031,6095],{},[1813,6032,6033,6035,6037,6039,6041,6043,6045,6047,6049,6051,6053,6055,6093],{},[1816,6034,2380],{},[1820,6036,2383],{"stretchy":1961},[1816,6038,1818],{},[1820,6040,1990],{},[1816,6042,4735],{},[1820,6044,2576],{},[1816,6046,1818],{},[1820,6048,1900],{},[1816,6050,4735],{},[1820,6052,2388],{"stretchy":1961},[1820,6054,1971],{},[1973,6056,6057,6079],{},[1813,6058,6059,6061,6063,6065,6067,6069,6071,6077],{},[1816,6060,2380],{},[1820,6062,2383],{"stretchy":1961},[1820,6064,1962],{"stretchy":1961},[1816,6066,1818],{},[1820,6068,1990],{},[1816,6070,4735],{},[4780,6072,6073,6075],{},[1820,6074,1968],{"stretchy":1961},[1820,6076,2570],{},[1820,6078,2388],{"stretchy":1961},[1813,6080,6081,6083,6085,6087,6089,6091],{},[1816,6082,2558],{},[1820,6084,1962],{"stretchy":1961},[1816,6086,1818],{},[1820,6088,1900],{},[1816,6090,4735],{},[1820,6092,1968],{"stretchy":1961},[1816,6094,2420],{"mathvariant":1995},[1828,6096,6097],{"encoding":1830},"E[X-d\\mid X>d]\n=\\frac{E[(X-d)_+]}{P(X>d)}.",[1797,6099,6101,6125,6143,6161,6182],{"className":6100,"ariaHidden":1836},[1835],[1797,6102,6104,6107,6110,6113,6116,6119,6122],{"className":6103},[1840],[1797,6105],{"className":6106,"style":2058},[1844],[1797,6108,2380],{"className":6109,"style":2436},[1849,1850],[1797,6111,2383],{"className":6112},[2066],[1797,6114,1818],{"className":6115,"style":1851},[1849,1850],[1797,6117],{"className":6118,"style":2644},[1855],[1797,6120,1990],{"className":6121},[2648],[1797,6123],{"className":6124,"style":2644},[1855],[1797,6126,6128,6131,6134,6137,6140],{"className":6127},[1840],[1797,6129],{"className":6130,"style":2058},[1844],[1797,6132,4735],{"className":6133},[1849,1850],[1797,6135],{"className":6136,"style":1856},[1855],[1797,6138,2576],{"className":6139},[1860],[1797,6141],{"className":6142,"style":1856},[1855],[1797,6144,6146,6149,6152,6155,6158],{"className":6145},[1840],[1797,6147],{"className":6148,"style":2676},[1844],[1797,6150,1818],{"className":6151,"style":1851},[1849,1850],[1797,6153],{"className":6154,"style":1856},[1855],[1797,6156,1900],{"className":6157},[1860],[1797,6159],{"className":6160,"style":1856},[1855],[1797,6162,6164,6167,6170,6173,6176,6179],{"className":6163},[1840],[1797,6165],{"className":6166,"style":2058},[1844],[1797,6168,4735],{"className":6169},[1849,1850],[1797,6171,2388],{"className":6172},[2073],[1797,6174],{"className":6175,"style":1856},[1855],[1797,6177,1971],{"className":6178},[1860],[1797,6180],{"className":6181,"style":1856},[1855],[1797,6183,6185,6189,6334],{"className":6184},[1840],[1797,6186],{"className":6187,"style":6188},[1844],"height:2.363em;vertical-align:-0.936em;",[1797,6190,6192,6195,6331],{"className":6191},[1849],[1797,6193],{"className":6194},[2066,2096],[1797,6196,6198],{"className":6197},[1973],[1797,6199,6201,6323],{"className":6200},[2103,2104],[1797,6202,6204,6320],{"className":6203},[2108],[1797,6205,6208,6240,6248],{"className":6206,"style":6207},[2112],"height:1.427em;",[1797,6209,6210,6213],{"style":2116},[1797,6211],{"className":6212,"style":2121},[2120],[1797,6214,6216,6219,6222,6225,6228,6231,6234,6237],{"className":6215},[1849],[1797,6217,2558],{"className":6218,"style":2252},[1849,1850],[1797,6220,1962],{"className":6221},[2066],[1797,6223,1818],{"className":6224,"style":1851},[1849,1850],[1797,6226],{"className":6227,"style":1856},[1855],[1797,6229,1900],{"className":6230},[1860],[1797,6232],{"className":6233,"style":1856},[1855],[1797,6235,4735],{"className":6236},[1849,1850],[1797,6238,1968],{"className":6239},[2073],[1797,6241,6242,6245],{"style":2130},[1797,6243],{"className":6244,"style":2121},[2120],[1797,6246],{"className":6247,"style":2138},[2137],[1797,6249,6250,6253],{"style":2141},[1797,6251],{"className":6252,"style":2121},[2120],[1797,6254,6256,6259,6262,6265,6268,6271,6274,6277,6317],{"className":6255},[1849],[1797,6257,2380],{"className":6258,"style":2436},[1849,1850],[1797,6260,5020],{"className":6261},[2066],[1797,6263,1818],{"className":6264,"style":1851},[1849,1850],[1797,6266],{"className":6267,"style":2644},[1855],[1797,6269,1990],{"className":6270},[2648],[1797,6272],{"className":6273,"style":2644},[1855],[1797,6275,4735],{"className":6276},[1849,1850],[1797,6278,6280,6283],{"className":6279},[2073],[1797,6281,1968],{"className":6282},[2073],[1797,6284,6286],{"className":6285},[2177],[1797,6287,6289,6309],{"className":6288},[2103,2104],[1797,6290,6292,6306],{"className":6291},[2108],[1797,6293,6295],{"className":6294,"style":4861},[2112],[1797,6296,6297,6300],{"style":4864},[1797,6298],{"className":6299,"style":2194},[2120],[1797,6301,6303],{"className":6302},[2198,2199,2200,2201],[1797,6304,2570],{"className":6305},[2648,2201],[1797,6307,2155],{"className":6308},[2154],[1797,6310,6312],{"className":6311},[2108],[1797,6313,6315],{"className":6314,"style":4883},[2112],[1797,6316],{},[1797,6318,2388],{"className":6319},[2073],[1797,6321,2155],{"className":6322},[2154],[1797,6324,6326],{"className":6325},[2108],[1797,6327,6329],{"className":6328,"style":3196},[2112],[1797,6330],{},[1797,6332],{"className":6333},[2073,2096],[1797,6335,2420],{"className":6336},[1849],[1793,6338,6339],{},"Do not confuse this with the unconditional payment per exposure or per ground-up loss.",[1876,6341,6343],{"id":6342},"_6-choose-a-model-by-consequence","6. Choose a model by consequence",[4325,6345,6346,6356],{},[4328,6347,6348],{},[4331,6349,6350,6353],{},[4334,6351,6352],{},"Task",[4334,6354,6355],{},"Most important checks",[4348,6357,6358,6366,6374,6382],{},[4331,6359,6360,6363],{},[4353,6361,6362],{},"ordinary claim budgeting",[4353,6364,6365],{},"mean, calibration by segment, out-of-sample error",[4331,6367,6368,6371],{},[4353,6369,6370],{},"deductible pricing",[4353,6372,6373],{},"probability above deductible and payment mean",[4331,6375,6376,6379],{},[4353,6377,6378],{},"high-layer reinsurance",[4353,6380,6381],{},"survival and mean excess near attachment",[4331,6383,6384,6387],{},[4353,6385,6386],{},"capital",[4353,6388,6389],{},"aggregate tail, dependence, parameter\u002Fmodel uncertainty",[1876,6391,6393],{"id":6392},"practice","Practice",[6395,6396,6397,6479,6482],"ol",{},[3322,6398,6399,6400,2420],{},"For Exponential mean £4,000, find ",[1797,6401,6403,6430],{"className":6402},[1800],[1797,6404,6406],{"className":6405},[1804],[1806,6407,6408],{"xmlns":1808},[1810,6409,6410,6427],{},[1813,6411,6412,6414,6416,6418,6420,6422,6425],{},[1816,6413,2558],{},[1820,6415,1962],{"stretchy":1961},[1816,6417,1818],{},[1820,6419,1900],{},[1816,6421,5535],{"mathvariant":1995},[1824,6423,6424],{},"10,000",[1820,6426,1968],{"stretchy":1961},[1828,6428,6429],{"encoding":1830},"P(X>£10{,}000)",[1797,6431,6433,6457],{"className":6432,"ariaHidden":1836},[1835],[1797,6434,6436,6439,6442,6445,6448,6451,6454],{"className":6435},[1840],[1797,6437],{"className":6438,"style":2058},[1844],[1797,6440,2558],{"className":6441,"style":2252},[1849,1850],[1797,6443,1962],{"className":6444},[2066],[1797,6446,1818],{"className":6447,"style":1851},[1849,1850],[1797,6449],{"className":6450,"style":1856},[1855],[1797,6452,1900],{"className":6453},[1860],[1797,6455],{"className":6456,"style":1856},[1855],[1797,6458,6460,6463,6467,6473,6476],{"className":6459},[1840],[1797,6461],{"className":6462,"style":2058},[1844],[1797,6464,6466],{"className":6465},[1849],"£10",[1797,6468,6470],{"className":6469},[1849],[1797,6471,1938],{"className":6472},[2220],[1797,6474,4421],{"className":6475},[1849],[1797,6477,1968],{"className":6478},[2073],[3322,6480,6481],{},"A Gamma model has shape 9 and mean £4,500. Find scale and coefficient of variation.",[3322,6483,6484],{},"Why can a model fit a histogram well but price a high layer badly?",[6486,6487,6489],"legacy-details",{"title":6488},"Answers",[6395,6490,6491,6673,6887],{},[3322,6492,6493,2420],{},[1797,6494,6496,6541],{"className":6495},[1800],[1797,6497,6499],{"className":6498},[1804],[1806,6500,6501],{"xmlns":1808},[1810,6502,6503,6538],{},[1813,6504,6505,6520,6522,6533,6535],{},[1981,6506,6507,6509],{},[1816,6508,1985],{},[1813,6510,6511,6513,6515,6517],{},[1820,6512,1990],{},[1824,6514,6424],{},[1816,6516,1996],{"mathvariant":1995},[1824,6518,6519],{},"4,000",[1820,6521,1971],{},[1981,6523,6524,6526],{},[1816,6525,1985],{},[1813,6527,6528,6530],{},[1820,6529,1990],{},[1824,6531,6532],{},"2.5",[1820,6534,5674],{},[1824,6536,6537],{},"0.0821",[1828,6539,6540],{"encoding":1830},"e^{-10{,}000\u002F4{,}000}=e^{-2.5}\\approx0.0821",[1797,6542,6544,6614,6664],{"className":6543,"ariaHidden":1836},[1835],[1797,6545,6547,6550,6605,6608,6611],{"className":6546},[1840],[1797,6548],{"className":6549,"style":3163},[1844],[1797,6551,6553,6556],{"className":6552},[1849],[1797,6554,1985],{"className":6555},[1849,1850],[1797,6557,6559],{"className":6558},[2177],[1797,6560,6562],{"className":6561},[2103],[1797,6563,6565],{"className":6564},[2108],[1797,6566,6568],{"className":6567,"style":3163},[2112],[1797,6569,6570,6573],{"style":3126},[1797,6571],{"className":6572,"style":2194},[2120],[1797,6574,6576],{"className":6575},[2198,2199,2200,2201],[1797,6577,6579,6582,6586,6592,6596,6602],{"className":6578},[1849,2201],[1797,6580,1990],{"className":6581},[1849,2201],[1797,6583,6585],{"className":6584},[1849,2201],"10",[1797,6587,6589],{"className":6588},[1849,2201],[1797,6590,1938],{"className":6591},[2220,2201],[1797,6593,6595],{"className":6594},[1849,2201],"000\u002F4",[1797,6597,6599],{"className":6598},[1849,2201],[1797,6600,1938],{"className":6601},[2220,2201],[1797,6603,4421],{"className":6604},[1849,2201],[1797,6606],{"className":6607,"style":1856},[1855],[1797,6609,1971],{"className":6610},[1860],[1797,6612],{"className":6613,"style":1856},[1855],[1797,6615,6617,6620,6655,6658,6661],{"className":6616},[1840],[1797,6618],{"className":6619,"style":3665},[1844],[1797,6621,6623,6626],{"className":6622},[1849],[1797,6624,1985],{"className":6625},[1849,1850],[1797,6627,6629],{"className":6628},[2177],[1797,6630,6632],{"className":6631},[2103],[1797,6633,6635],{"className":6634},[2108],[1797,6636,6638],{"className":6637,"style":3665},[2112],[1797,6639,6640,6643],{"style":3126},[1797,6641],{"className":6642,"style":2194},[2120],[1797,6644,6646],{"className":6645},[2198,2199,2200,2201],[1797,6647,6649,6652],{"className":6648},[1849,2201],[1797,6650,1990],{"className":6651},[1849,2201],[1797,6653,6532],{"className":6654},[1849,2201],[1797,6656],{"className":6657,"style":1856},[1855],[1797,6659,5674],{"className":6660},[1860],[1797,6662],{"className":6663,"style":1856},[1855],[1797,6665,6667,6670],{"className":6666},[1840],[1797,6668],{"className":6669,"style":1870},[1844],[1797,6671,6537],{"className":6672},[1849],[3322,6674,6675,6676,6761,6762,2420],{},"Scale ",[1797,6677,6679,6708],{"className":6678},[1800],[1797,6680,6682],{"className":6681},[1804],[1806,6683,6684],{"xmlns":1808},[1810,6685,6686,6705],{},[1813,6687,6688,6690,6693,6695,6698,6700,6702],{},[1820,6689,1971],{},[1824,6691,6692],{},"4,500",[1816,6694,1996],{"mathvariant":1995},[1824,6696,6697],{},"9",[1820,6699,1971],{},[1816,6701,5535],{"mathvariant":1995},[1824,6703,6704],{},"500",[1828,6706,6707],{"encoding":1830},"=4{,}500\u002F9=£500",[1797,6709,6711,6723,6751],{"className":6710,"ariaHidden":1836},[1835],[1797,6712,6714,6717,6720],{"className":6713},[1840],[1797,6715],{"className":6716,"style":4582},[1844],[1797,6718,1971],{"className":6719},[1860],[1797,6721],{"className":6722,"style":1856},[1855],[1797,6724,6726,6729,6732,6738,6742,6745,6748],{"className":6725},[1840],[1797,6727],{"className":6728,"style":2058},[1844],[1797,6730,4453],{"className":6731},[1849],[1797,6733,6735],{"className":6734},[1849],[1797,6736,1938],{"className":6737},[2220],[1797,6739,6741],{"className":6740},[1849],"500\u002F9",[1797,6743],{"className":6744,"style":1856},[1855],[1797,6746,1971],{"className":6747},[1860],[1797,6749],{"className":6750,"style":1856},[1855],[1797,6752,6754,6757],{"className":6753},[1840],[1797,6755],{"className":6756,"style":3354},[1844],[1797,6758,6760],{"className":6759},[1849],"£500","; CV ",[1797,6763,6765,6796],{"className":6764},[1800],[1797,6766,6768],{"className":6767},[1804],[1806,6769,6770],{"xmlns":1808},[1810,6771,6772,6793],{},[1813,6773,6774,6776,6778,6780,6784,6786,6788,6790],{},[1820,6775,1971],{},[1824,6777,1977],{},[1816,6779,1996],{"mathvariant":1995},[3451,6781,6782],{},[1824,6783,6697],{},[1820,6785,1971],{},[1824,6787,1977],{},[1816,6789,1996],{"mathvariant":1995},[1824,6791,6792],{},"3",[1828,6794,6795],{"encoding":1830},"=1\u002F\\sqrt9=1\u002F3",[1797,6797,6799,6811,6877],{"className":6798,"ariaHidden":1836},[1835],[1797,6800,6802,6805,6808],{"className":6801},[1840],[1797,6803],{"className":6804,"style":4582},[1844],[1797,6806,1971],{"className":6807},[1860],[1797,6809],{"className":6810,"style":1856},[1855],[1797,6812,6814,6818,6821,6868,6871,6874],{"className":6813},[1840],[1797,6815],{"className":6816,"style":6817},[1844],"height:1.1572em;vertical-align:-0.25em;",[1797,6819,3471],{"className":6820},[1849],[1797,6822,6824],{"className":6823},[1849,3475],[1797,6825,6827,6859],{"className":6826},[2103,2104],[1797,6828,6830,6856],{"className":6829},[2108],[1797,6831,6834,6843],{"className":6832,"style":6833},[2112],"height:0.9072em;",[1797,6835,6837,6840],{"className":6836,"style":2245},[3489],[1797,6838],{"className":6839,"style":2121},[2120],[1797,6841,6697],{"className":6842,"style":3496},[1849],[1797,6844,6846,6849],{"style":6845},"top:-2.8672em;",[1797,6847],{"className":6848,"style":2121},[2120],[1797,6850,6852],{"className":6851,"style":3510},[3509],[3512,6853,6854],{"xmlns":3514,"width":3515,"height":3516,"viewBox":3517,"preserveAspectRatio":3518},[3520,6855],{"d":3522},[1797,6857,2155],{"className":6858},[2154],[1797,6860,6862],{"className":6861},[2108],[1797,6863,6866],{"className":6864,"style":6865},[2112],"height:0.1328em;",[1797,6867],{},[1797,6869],{"className":6870,"style":1856},[1855],[1797,6872,1971],{"className":6873},[1860],[1797,6875],{"className":6876,"style":1856},[1855],[1797,6878,6880,6883],{"className":6879},[1840],[1797,6881],{"className":6882,"style":2058},[1844],[1797,6884,6886],{"className":6885},[1849],"1\u002F3",[3322,6888,6889],{},"Most histogram mass is in the body; few tail observations determine high-layer cost. Tail diagnostics and uncertainty must be assessed separately.",[1793,6891,6892,6893,2420],{},"Continue to ",[6894,6895,6897],"a",{"href":6896},".\u002F02-more-dist","Pareto, Weibull, and extreme-value models",{"title":10,"searchDepth":6899,"depth":6899,"links":6900},2,[6901,6902,6903,6904,6905,6911,6912],{"id":1878,"depth":6899,"text":1879},{"id":2754,"depth":6899,"text":2755},{"id":3541,"depth":6899,"text":3542},{"id":4319,"depth":6899,"text":4320},{"id":4711,"depth":6899,"text":4712,"children":6906},[6907,6909,6910],{"id":4716,"depth":6908,"text":4717},3,{"id":5771,"depth":6908,"text":5772},{"id":6009,"depth":6908,"text":6010},{"id":6342,"depth":6899,"text":6343},{"id":6392,"depth":6899,"text":6393},"Compare Exponential, Gamma, and lognormal claim models through moments, quantiles, and layer costs.","md",{"sidebar":6916},{"order":6917},1,true,{"title":864,"description":6913},"jqsYsl9aANcSVoLOdtG31h1a4sQPFfADmqxhd4-hyHE",[6922,6924],{"title":858,"path":859,"stem":860,"description":6923,"children":-1},"Select loss models from the insurance question, observation process, and tail—not from a distribution list.",{"title":868,"path":869,"stem":870,"description":6925,"children":-1},"Model large losses with Weibull, Pareto, and threshold exceedances while making tail uncertainty visible.",1785754734711]