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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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These are separate steps.",[1797,1798,1800],"h2",{"id":1799},"_1-audit-the-sample","1. Audit the sample",[1793,1802,1803],{},"Before fitting, answer:",[1805,1806,1807,1811,1814,1817,1820,1823],"ol",{},[1808,1809,1810],"li",{},"Are amounts at a common price and currency level?",[1808,1812,1813],{},"Are losses ground-up or payments after deductible and limit?",[1808,1815,1816],{},"Are limit observations censored or genuinely equal to the limit?",[1808,1818,1819],{},"Are small losses absent because of truncation or because none occurred?",[1808,1821,1822],{},"Are claims independent, or clustered within events and policyholders?",[1808,1824,1825],{},"Was the sample selected using information unavailable at prediction time?",[1793,1827,1828,1829,1833],{},"The likelihood must describe the ",[1830,1831,1832],"strong",{},"observation process",", not only the latent ground-up loss.",[1797,1835,1837],{"id":1836},"_2-likelihood-contributions","2. Likelihood contributions",[1793,1839,1840,1841,2027,2028,1875],{},"For exact independent observations ",[1842,1843,1846,1893],"span",{"className":1844},[1845],"katex",[1842,1847,1850],{"className":1848},[1849],"katex-mathml",[1851,1852,1854],"math",{"xmlns":1853},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1855,1856,1857,1888],"semantics",{},[1858,1859,1860,1871,1876,1879,1881],"mrow",{},[1861,1862,1863,1867],"msub",{},[1864,1865,1866],"mi",{},"x",[1868,1869,1870],"mn",{},"1",[1872,1873,1875],"mo",{"separator":1874},"true",",",[1872,1877,1878],{},"…",[1872,1880,1875],{"separator":1874},[1861,1882,1883,1885],{},[1864,1884,1866],{},[1864,1886,1887],{},"n",[1889,1890,1892],"annotation",{"encoding":1891},"application\u002Fx-tex","x_1,\\ldots,x_n",[1842,1894,1897],{"className":1895,"ariaHidden":1874},[1896],"katex-html",[1842,1898,1901,1906,1964,1968,1973,1977,1980,1983,1986],{"className":1899},[1900],"base",[1842,1902],{"className":1903,"style":1905},[1904],"strut","height:0.625em;vertical-align:-0.1944em;",[1842,1907,1910,1914],{"className":1908},[1909],"mord",[1842,1911,1866],{"className":1912},[1909,1913],"mathnormal",[1842,1915,1918],{"className":1916},[1917],"msupsub",[1842,1919,1923,1955],{"className":1920},[1921,1922],"vlist-t","vlist-t2",[1842,1924,1927,1950],{"className":1925},[1926],"vlist-r",[1842,1928,1932],{"className":1929,"style":1931},[1930],"vlist","height:0.3011em;",[1842,1933,1935,1940],{"style":1934},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1842,1936],{"className":1937,"style":1939},[1938],"pstrut","height:2.7em;",[1842,1941,1947],{"className":1942},[1943,1944,1945,1946],"sizing","reset-size6","size3","mtight",[1842,1948,1870],{"className":1949},[1909,1946],[1842,1951,1954],{"className":1952},[1953],"vlist-s","​",[1842,1956,1958],{"className":1957},[1926],[1842,1959,1962],{"className":1960,"style":1961},[1930],"height:0.15em;",[1842,1963],{},[1842,1965,1875],{"className":1966},[1967],"mpunct",[1842,1969],{"className":1970,"style":1972},[1971],"mspace","margin-right:0.1667em;",[1842,1974,1878],{"className":1975},[1976],"minner",[1842,1978],{"className":1979,"style":1972},[1971],[1842,1981,1875],{"className":1982},[1967],[1842,1984],{"className":1985,"style":1972},[1971],[1842,1987,1989,1992],{"className":1988},[1909],[1842,1990,1866],{"className":1991},[1909,1913],[1842,1993,1995],{"className":1994},[1917],[1842,1996,1998,2019],{"className":1997},[1921,1922],[1842,1999,2001,2016],{"className":2000},[1926],[1842,2002,2005],{"className":2003,"style":2004},[1930],"height:0.1514em;",[1842,2006,2007,2010],{"style":1934},[1842,2008],{"className":2009,"style":1939},[1938],[1842,2011,2013],{"className":2012},[1943,1944,1945,1946],[1842,2014,1887],{"className":2015},[1909,1913,1946],[1842,2017,1954],{"className":2018},[1953],[1842,2020,2022],{"className":2021},[1926],[1842,2023,2025],{"className":2024,"style":1961},[1930],[1842,2026],{}," with density 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truncation at threshold ",[1842,2366,2368,2382],{"className":2367},[1845],[1842,2369,2371],{"className":2370},[1849],[1851,2372,2373],{"xmlns":1853},[1855,2374,2375,2380],{},[1858,2376,2377],{},[1864,2378,2379],{},"d",[1889,2381,2379],{"encoding":1891},[1842,2383,2385],{"className":2384,"ariaHidden":1874},[1896],[1842,2386,2388,2392],{"className":2387},[1900],[1842,2389],{"className":2390,"style":2391},[1904],"height:0.6944em;",[1842,2393,2379],{"className":2394},[1909,1913],[1793,2396,2397,2398,2453],{},"If only claims with ",[1842,2399,2401,2421],{"className":2400},[1845],[1842,2402,2404],{"className":2403},[1849],[1851,2405,2406],{"xmlns":1853},[1855,2407,2408,2418],{},[1858,2409,2410,2413,2416],{},[1864,2411,2412],{},"X",[1872,2414,2415],{},">",[1864,2417,2379],{},[1889,2419,2420],{"encoding":1891},"X>d",[1842,2422,2424,2444],{"className":2423,"ariaHidden":1874},[1896],[1842,2425,2427,2431,2435,2438,2441],{"className":2426},[1900],[1842,2428],{"className":2429,"style":2430},[1904],"height:0.7224em;vertical-align:-0.0391em;",[1842,2432,2412],{"className":2433,"style":2434},[1909,1913],"margin-right:0.0785em;",[1842,2436],{"className":2437,"style":2195},[1971],[1842,2439,2415],{"className":2440},[2199],[1842,2442],{"className":2443,"style":2195},[1971],[1842,2445,2447,2450],{"className":2446},[1900],[1842,2448],{"className":2449,"style":2391},[1904],[1842,2451,2379],{"className":2452},[1909,1913]," enter the dataset and their ground-up values are observed, each contribution is",[1842,2455,2457],{"className":2456},[2099],[1842,2458,2460,2572],{"className":2459},[1845],[1842,2461,2463],{"className":2462},[1849],[1851,2464,2465],{"xmlns":1853,"display":2108},[1855,2466,2467,2569],{},[1858,2468,2469,2509,2511,2552,2554,2557,2563,2565,2567],{},[2470,2471,2472,2490],"mfrac",{},[1858,2473,2474,2476,2478,2484,2486,2488],{},[1864,2475,2042],{},[1872,2477,2046],{"stretchy":2045},[1861,2479,2480,2482],{},[1864,2481,1866],{},[1864,2483,2136],{},[1872,2485,2051],{"separator":1874},[1864,2487,2054],{},[1872,2489,2057],{"stretchy":2045},[1858,2491,2492,2499,2501,2503,2505,2507],{},[1861,2493,2494,2497],{},[1864,2495,2496],{},"P",[1864,2498,2054],{},[1872,2500,2046],{"stretchy":2045},[1864,2502,2412],{},[1872,2504,2415],{},[1864,2506,2379],{},[1872,2508,2057],{"stretchy":2045},[1872,2510,2125],{},[2470,2512,2513,2531],{},[1858,2514,2515,2517,2519,2525,2527,2529],{},[1864,2516,2042],{},[1872,2518,2046],{"stretchy":2045},[1861,2520,2521,2523],{},[1864,2522,1866],{},[1864,2524,2136],{},[1872,2526,2051],{"separator":1874},[1864,2528,2054],{},[1872,2530,2057],{"stretchy":2045},[1858,2532,2533,2542,2544,2546,2548,2550],{},[2534,2535,2536,2539],"mover",{"accent":1874},[1864,2537,2538],{},"F",[1872,2540,2541],{},"ˉ",[1872,2543,2046],{"stretchy":2045},[1864,2545,2379],{},[1872,2547,2051],{"separator":1874},[1864,2549,2054],{},[1872,2551,2057],{"stretchy":2045},[1872,2553,1875],{"separator":1874},[1971,2555],{"width":2556},"2em",[1861,2558,2559,2561],{},[1864,2560,1866],{},[1864,2562,2136],{},[1872,2564,2415],{},[1864,2566,2379],{},[1864,2568,2167],{"mathvariant":2115},[1889,2570,2571],{"encoding":1891},"\\frac{f(x_i;\\theta)}{P_\\theta(X>d)}\n=\\frac{f(x_i;\\theta)}{\\bar F(d;\\theta)},\n\\qquad x_i>d.",[1842,2573,2575,2778,3015],{"className":2574,"ariaHidden":1874},[1896],[1842,2576,2578,2582,2769,2772,2775],{"className":2577},[1900],[1842,2579],{"className":2580,"style":2581},[1904],"height:2.363em;vertical-align:-0.936em;",[1842,2583,2585,2589,2766],{"className":2584},[1909],[1842,2586],{"className":2587},[2078,2588],"nulldelimiter",[1842,2590,2592],{"className":2591},[2470],[1842,2593,2595,2757],{"className":2594},[1921,1922],[1842,2596,2598,2754],{"className":2597},[1926],[1842,2599,2602,2676,2687],{"className":2600,"style":2601},[1930],"height:1.427em;",[1842,2603,2605,2609],{"style":2604},"top:-2.314em;",[1842,2606],{"className":2607,"style":2608},[1938],"height:3em;",[1842,2610,2612,2655,2658,2661,2664,2667,2670,2673],{"className":2611},[1909],[1842,2613,2615,2619],{"className":2614},[1909],[1842,2616,2496],{"className":2617,"style":2618},[1909,1913],"margin-right:0.1389em;",[1842,2620,2622],{"className":2621},[1917],[1842,2623,2625,2647],{"className":2624},[1921,1922],[1842,2626,2628,2644],{"className":2627},[1926],[1842,2629,2632],{"className":2630,"style":2631},[1930],"height:0.3361em;",[1842,2633,2635,2638],{"style":2634},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1842,2636],{"className":2637,"style":1939},[1938],[1842,2639,2641],{"className":2640},[1943,1944,1945,1946],[1842,2642,2054],{"className":2643,"style":2091},[1909,1913,1946],[1842,2645,1954],{"className":2646},[1953],[1842,2648,2650],{"className":2649},[1926],[1842,2651,2653],{"className":2652,"style":1961},[1930],[1842,2654],{},[1842,2656,2046],{"className":2657},[2078],[1842,2659,2412],{"className":2660,"style":2434},[1909,1913],[1842,2662],{"className":2663,"style":2195},[1971],[1842,2665,2415],{"className":2666},[2199],[1842,2668],{"className":2669,"style":2195},[1971],[1842,2671,2379],{"className":2672},[1909,1913],[1842,2674,2057],{"className":2675},[2095],[1842,2677,2679,2682],{"style":2678},"top:-3.23em;",[1842,2680],{"className":2681,"style":2608},[1938],[1842,2683],{"className":2684,"style":2686},[2685],"frac-line","border-bottom-width:0.04em;",[1842,2688,2690,2693],{"style":2689},"top:-3.677em;",[1842,2691],{"className":2692,"style":2608},[1938],[1842,2694,2696,2699,2702,2742,2745,2748,2751],{"className":2695},[1909],[1842,2697,2042],{"className":2698,"style":2074},[1909,1913],[1842,2700,2046],{"className":2701},[2078],[1842,2703,2705,2708],{"className":2704},[1909],[1842,2706,1866],{"className":2707},[1909,1913],[1842,2709,2711],{"className":2710},[1917],[1842,2712,2714,2734],{"className":2713},[1921,1922],[1842,2715,2717,2731],{"className":2716},[1926],[1842,2718,2720],{"className":2719,"style":2322},[1930],[1842,2721,2722,2725],{"style":1934},[1842,2723],{"className":2724,"style":1939},[1938],[1842,2726,2728],{"className":2727},[1943,1944,1945,1946],[1842,2729,2136],{"className":2730},[1909,1913,1946],[1842,2732,1954],{"className":2733},[1953],[1842,2735,2737],{"className":2736},[1926],[1842,2738,2740],{"className":2739,"style":1961},[1930],[1842,2741],{},[1842,2743,2051],{"className":2744},[1967],[1842,2746],{"className":2747,"style":1972},[1971],[1842,2749,2054],{"className":2750,"style":2091},[1909,1913],[1842,2752,2057],{"className":2753},[2095],[1842,2755,1954],{"className":2756},[1953],[1842,2758,2760],{"className":2759},[1926],[1842,2761,2764],{"className":2762,"style":2763},[1930],"height:0.936em;",[1842,2765],{},[1842,2767],{"className":2768},[2095,2588],[1842,2770],{"className":2771,"style":2195},[1971],[1842,2773,2125],{"className":2774},[2199],[1842,2776],{"className":2777,"style":2195},[1971],[1842,2779,2781,2785,2956,2959,2963,2966,3006,3009,3012],{"className":2780},[1900],[1842,2782],{"className":2783,"style":2784},[1904],"height:2.3871em;vertical-align:-0.9601em;",[1842,2786,2788,2791,2953],{"className":2787},[1909],[1842,2789],{"className":2790},[2078,2588],[1842,2792,2794],{"className":2793},[2470],[1842,2795,2797,2944],{"className":2796},[1921,1922],[1842,2798,2800,2941],{"className":2799},[1926],[1842,2801,2803,2867,2875],{"className":2802,"style":2601},[1930],[1842,2804,2806,2809],{"style":2805},"top:-2.2899em;",[1842,2807],{"className":2808,"style":2608},[1938],[1842,2810,2812,2849,2852,2855,2858,2861,2864],{"className":2811},[1909],[1842,2813,2816],{"className":2814},[1909,2815],"accent",[1842,2817,2819],{"className":2818},[1921],[1842,2820,2822],{"className":2821},[1926],[1842,2823,2826,2835],{"className":2824,"style":2825},[1930],"height:0.8201em;",[1842,2827,2829,2832],{"style":2828},"top:-3em;",[1842,2830],{"className":2831,"style":2608},[1938],[1842,2833,2538],{"className":2834,"style":2618},[1909,1913],[1842,2836,2838,2841],{"style":2837},"top:-3.2523em;",[1842,2839],{"className":2840,"style":2608},[1938],[1842,2842,2846],{"className":2843,"style":2845},[2844],"accent-body","left:-0.1667em;",[1842,2847,2541],{"className":2848},[1909],[1842,2850,2046],{"className":2851},[2078],[1842,2853,2379],{"className":2854},[1909,1913],[1842,2856,2051],{"className":2857},[1967],[1842,2859],{"className":2860,"style":1972},[1971],[1842,2862,2054],{"className":2863,"style":2091},[1909,1913],[1842,2865,2057],{"className":2866},[2095],[1842,2868,2869,2872],{"style":2678},[1842,2870],{"className":2871,"style":2608},[1938],[1842,2873],{"className":2874,"style":2686},[2685],[1842,2876,2877,2880],{"style":2689},[1842,2878],{"className":2879,"style":2608},[1938],[1842,2881,2883,2886,2889,2929,2932,2935,2938],{"className":2882},[1909],[1842,2884,2042],{"className":2885,"style":2074},[1909,1913],[1842,2887,2046],{"className":2888},[2078],[1842,2890,2892,2895],{"className":2891},[1909],[1842,2893,1866],{"className":2894},[1909,1913],[1842,2896,2898],{"className":2897},[1917],[1842,2899,2901,2921],{"className":2900},[1921,1922],[1842,2902,2904,2918],{"className":2903},[1926],[1842,2905,2907],{"className":2906,"style":2322},[1930],[1842,2908,2909,2912],{"style":1934},[1842,2910],{"className":2911,"style":1939},[1938],[1842,2913,2915],{"className":2914},[1943,1944,1945,1946],[1842,2916,2136],{"className":2917},[1909,1913,1946],[1842,2919,1954],{"className":2920},[1953],[1842,2922,2924],{"className":2923},[1926],[1842,2925,2927],{"className":2926,"style":1961},[1930],[1842,2928],{},[1842,2930,2051],{"className":2931},[1967],[1842,2933],{"className":2934,"style":1972},[1971],[1842,2936,2054],{"className":2937,"style":2091},[1909,1913],[1842,2939,2057],{"className":2940},[2095],[1842,2942,1954],{"className":2943},[1953],[1842,2945,2947],{"className":2946},[1926],[1842,2948,2951],{"className":2949,"style":2950},[1930],"height:0.9601em;",[1842,2952],{},[1842,2954],{"className":2955},[2095,2588],[1842,2957,1875],{"className":2958},[1967],[1842,2960],{"className":2961,"style":2962},[1971],"margin-right:2em;",[1842,2964],{"className":2965,"style":1972},[1971],[1842,2967,2969,2972],{"className":2968},[1909],[1842,2970,1866],{"className":2971},[1909,1913],[1842,2973,2975],{"className":2974},[1917],[1842,2976,2978,2998],{"className":2977},[1921,1922],[1842,2979,2981,2995],{"className":2980},[1926],[1842,2982,2984],{"className":2983,"style":2322},[1930],[1842,2985,2986,2989],{"style":1934},[1842,2987],{"className":2988,"style":1939},[1938],[1842,2990,2992],{"className":2991},[1943,1944,1945,1946],[1842,2993,2136],{"className":2994},[1909,1913,1946],[1842,2996,1954],{"className":2997},[1953],[1842,2999,3001],{"className":3000},[1926],[1842,3002,3004],{"className":3003,"style":1961},[1930],[1842,3005],{},[1842,3007],{"className":3008,"style":2195},[1971],[1842,3010,2415],{"className":3011},[2199],[1842,3013],{"className":3014,"style":2195},[1971],[1842,3016,3018,3021,3024],{"className":3017},[1900],[1842,3019],{"className":3020,"style":2391},[1904],[1842,3022,2379],{"className":3023},[1909,1913],[1842,3025,2167],{"className":3026},[1909],[1793,3028,3029],{},"Ignoring the denominator treats a selected large-loss sample as representative of all losses.",[2361,3031,3033,3034],{"id":3032},"right-censoring-at-limit-uuu","Right censoring at limit ",[1842,3035,3037,3051],{"className":3036},[1845],[1842,3038,3040],{"className":3039},[1849],[1851,3041,3042],{"xmlns":1853},[1855,3043,3044,3049],{},[1858,3045,3046],{},[1864,3047,3048],{},"u",[1889,3050,3048],{"encoding":1891},[1842,3052,3054],{"className":3053,"ariaHidden":1874},[1896],[1842,3055,3057,3061],{"className":3056},[1900],[1842,3058],{"className":3059,"style":3060},[1904],"height:0.4306em;",[1842,3062,3048],{"className":3063},[1909,1913],[1793,3065,3066,3067,3095,3096,3194,3195,3095,3248,3338,3339,3367],{},"An exact value below ",[1842,3068,3070,3083],{"className":3069},[1845],[1842,3071,3073],{"className":3072},[1849],[1851,3074,3075],{"xmlns":1853},[1855,3076,3077,3081],{},[1858,3078,3079],{},[1864,3080,3048],{},[1889,3082,3048],{"encoding":1891},[1842,3084,3086],{"className":3085,"ariaHidden":1874},[1896],[1842,3087,3089,3092],{"className":3088},[1900],[1842,3090],{"className":3091,"style":3060},[1904],[1842,3093,3048],{"className":3094},[1909,1913]," contributes ",[1842,3097,3099,3127],{"className":3098},[1845],[1842,3100,3102],{"className":3101},[1849],[1851,3103,3104],{"xmlns":1853},[1855,3105,3106,3124],{},[1858,3107,3108,3110,3112,3118,3120,3122],{},[1864,3109,2042],{},[1872,3111,2046],{"stretchy":2045},[1861,3113,3114,3116],{},[1864,3115,1866],{},[1864,3117,2136],{},[1872,3119,2051],{"separator":1874},[1864,3121,2054],{},[1872,3123,2057],{"stretchy":2045},[1889,3125,3126],{"encoding":1891},"f(x_i;\\theta)",[1842,3128,3130],{"className":3129,"ariaHidden":1874},[1896],[1842,3131,3133,3136,3139,3142,3182,3185,3188,3191],{"className":3132},[1900],[1842,3134],{"className":3135,"style":2070},[1904],[1842,3137,2042],{"className":3138,"style":2074},[1909,1913],[1842,3140,2046],{"className":3141},[2078],[1842,3143,3145,3148],{"className":3144},[1909],[1842,3146,1866],{"className":3147},[1909,1913],[1842,3149,3151],{"className":3150},[1917],[1842,3152,3154,3174],{"className":3153},[1921,1922],[1842,3155,3157,3171],{"className":3156},[1926],[1842,3158,3160],{"className":3159,"style":2322},[1930],[1842,3161,3162,3165],{"style":1934},[1842,3163],{"className":3164,"style":1939},[1938],[1842,3166,3168],{"className":3167},[1943,1944,1945,1946],[1842,3169,2136],{"className":3170},[1909,1913,1946],[1842,3172,1954],{"className":3173},[1953],[1842,3175,3177],{"className":3176},[1926],[1842,3178,3180],{"className":3179,"style":1961},[1930],[1842,3181],{},[1842,3183,2051],{"className":3184},[1967],[1842,3186],{"className":3187,"style":1972},[1971],[1842,3189,2054],{"className":3190,"style":2091},[1909,1913],[1842,3192,2057],{"className":3193},[2095],"; an observation known only to satisfy ",[1842,3196,3198,3217],{"className":3197},[1845],[1842,3199,3201],{"className":3200},[1849],[1851,3202,3203],{"xmlns":1853},[1855,3204,3205,3214],{},[1858,3206,3207,3209,3212],{},[1864,3208,2412],{},[1872,3210,3211],{},"≥",[1864,3213,3048],{},[1889,3215,3216],{"encoding":1891},"X\\ge u",[1842,3218,3220,3239],{"className":3219,"ariaHidden":1874},[1896],[1842,3221,3223,3227,3230,3233,3236],{"className":3222},[1900],[1842,3224],{"className":3225,"style":3226},[1904],"height:0.8193em;vertical-align:-0.136em;",[1842,3228,2412],{"className":3229,"style":2434},[1909,1913],[1842,3231],{"className":3232,"style":2195},[1971],[1842,3234,3211],{"className":3235},[2199],[1842,3237],{"className":3238,"style":2195},[1971],[1842,3240,3242,3245],{"className":3241},[1900],[1842,3243],{"className":3244,"style":3060},[1904],[1842,3246,3048],{"className":3247},[1909,1913],[1842,3249,3251,3279],{"className":3250},[1845],[1842,3252,3254],{"className":3253},[1849],[1851,3255,3256],{"xmlns":1853},[1855,3257,3258,3276],{},[1858,3259,3260,3266,3268,3270,3272,3274],{},[2534,3261,3262,3264],{"accent":1874},[1864,3263,2538],{},[1872,3265,2541],{},[1872,3267,2046],{"stretchy":2045},[1864,3269,3048],{},[1872,3271,2051],{"separator":1874},[1864,3273,2054],{},[1872,3275,2057],{"stretchy":2045},[1889,3277,3278],{"encoding":1891},"\\bar F(u;\\theta)",[1842,3280,3282],{"className":3281,"ariaHidden":1874},[1896],[1842,3283,3285,3289,3320,3323,3326,3329,3332,3335],{"className":3284},[1900],[1842,3286],{"className":3287,"style":3288},[1904],"height:1.0701em;vertical-align:-0.25em;",[1842,3290,3292],{"className":3291},[1909,2815],[1842,3293,3295],{"className":3294},[1921],[1842,3296,3298],{"className":3297},[1926],[1842,3299,3301,3309],{"className":3300,"style":2825},[1930],[1842,3302,3303,3306],{"style":2828},[1842,3304],{"className":3305,"style":2608},[1938],[1842,3307,2538],{"className":3308,"style":2618},[1909,1913],[1842,3310,3311,3314],{"style":2837},[1842,3312],{"className":3313,"style":2608},[1938],[1842,3315,3317],{"className":3316,"style":2845},[2844],[1842,3318,2541],{"className":3319},[1909],[1842,3321,2046],{"className":3322},[2078],[1842,3324,3048],{"className":3325},[1909,1913],[1842,3327,2051],{"className":3328},[1967],[1842,3330],{"className":3331,"style":1972},[1971],[1842,3333,2054],{"className":3334,"style":2091},[1909,1913],[1842,3336,2057],{"className":3337},[2095],". Replacing every limited payment by an exact loss of ",[1842,3340,3342,3355],{"className":3341},[1845],[1842,3343,3345],{"className":3344},[1849],[1851,3346,3347],{"xmlns":1853},[1855,3348,3349,3353],{},[1858,3350,3351],{},[1864,3352,3048],{},[1889,3354,3048],{"encoding":1891},[1842,3356,3358],{"className":3357,"ariaHidden":1874},[1896],[1842,3359,3361,3364],{"className":3360},[1900],[1842,3362],{"className":3363,"style":3060},[1904],[1842,3365,3048],{"className":3366},[1909,1913]," understates the ground-up tail.",[2361,3369,3371],{"id":3370},"deductible-payment-data","Deductible payment data",[1793,3373,3374,3375,3454,3455,3505,3506,3534,3535,3563,3564,2167],{},"If recorded payment is ",[1842,3376,3378,3402],{"className":3377},[1845],[1842,3379,3381],{"className":3380},[1849],[1851,3382,3383],{"xmlns":1853},[1855,3384,3385,3399],{},[1858,3386,3387,3390,3392,3394,3397],{},[1864,3388,3389],{},"Y",[1872,3391,2125],{},[1864,3393,2412],{},[1872,3395,3396],{},"−",[1864,3398,2379],{},[1889,3400,3401],{"encoding":1891},"Y=X-d",[1842,3403,3405,3425,3445],{"className":3404,"ariaHidden":1874},[1896],[1842,3406,3408,3412,3416,3419,3422],{"className":3407},[1900],[1842,3409],{"className":3410,"style":3411},[1904],"height:0.6833em;",[1842,3413,3389],{"className":3414,"style":3415},[1909,1913],"margin-right:0.2222em;",[1842,3417],{"className":3418,"style":2195},[1971],[1842,3420,2125],{"className":3421},[2199],[1842,3423],{"className":3424,"style":2195},[1971],[1842,3426,3428,3432,3435,3438,3442],{"className":3427},[1900],[1842,3429],{"className":3430,"style":3431},[1904],"height:0.7667em;vertical-align:-0.0833em;",[1842,3433,2412],{"className":3434,"style":2434},[1909,1913],[1842,3436],{"className":3437,"style":3415},[1971],[1842,3439,3396],{"className":3440},[3441],"mbin",[1842,3443],{"className":3444,"style":3415},[1971],[1842,3446,3448,3451],{"className":3447},[1900],[1842,3449],{"className":3450,"style":2391},[1904],[1842,3452,2379],{"className":3453},[1909,1913]," conditional on ",[1842,3456,3458,3475],{"className":3457},[1845],[1842,3459,3461],{"className":3460},[1849],[1851,3462,3463],{"xmlns":1853},[1855,3464,3465,3473],{},[1858,3466,3467,3469,3471],{},[1864,3468,2412],{},[1872,3470,2415],{},[1864,3472,2379],{},[1889,3474,2420],{"encoding":1891},[1842,3476,3478,3496],{"className":3477,"ariaHidden":1874},[1896],[1842,3479,3481,3484,3487,3490,3493],{"className":3480},[1900],[1842,3482],{"className":3483,"style":2430},[1904],[1842,3485,2412],{"className":3486,"style":2434},[1909,1913],[1842,3488],{"className":3489,"style":2195},[1971],[1842,3491,2415],{"className":3492},[2199],[1842,3494],{"className":3495,"style":2195},[1971],[1842,3497,3499,3502],{"className":3498},[1900],[1842,3500],{"className":3501,"style":2391},[1904],[1842,3503,2379],{"className":3504},[1909,1913],", derive the density of ",[1842,3507,3509,3522],{"className":3508},[1845],[1842,3510,3512],{"className":3511},[1849],[1851,3513,3514],{"xmlns":1853},[1855,3515,3516,3520],{},[1858,3517,3518],{},[1864,3519,3389],{},[1889,3521,3389],{"encoding":1891},[1842,3523,3525],{"className":3524,"ariaHidden":1874},[1896],[1842,3526,3528,3531],{"className":3527},[1900],[1842,3529],{"className":3530,"style":3411},[1904],[1842,3532,3389],{"className":3533,"style":3415},[1909,1913]," from the conditional loss distribution. Do not fit ",[1842,3536,3538,3551],{"className":3537},[1845],[1842,3539,3541],{"className":3540},[1849],[1851,3542,3543],{"xmlns":1853},[1855,3544,3545,3549],{},[1858,3546,3547],{},[1864,3548,3389],{},[1889,3550,3389],{"encoding":1891},[1842,3552,3554],{"className":3553,"ariaHidden":1874},[1896],[1842,3555,3557,3560],{"className":3556},[1900],[1842,3558],{"className":3559,"style":3411},[1904],[1842,3561,3389],{"className":3562,"style":3415},[1909,1913]," as if it were ground-up ",[1842,3565,3567,3580],{"className":3566},[1845],[1842,3568,3570],{"className":3569},[1849],[1851,3571,3572],{"xmlns":1853},[1855,3573,3574,3578],{},[1858,3575,3576],{},[1864,3577,2412],{},[1889,3579,2412],{"encoding":1891},[1842,3581,3583],{"className":3582,"ariaHidden":1874},[1896],[1842,3584,3586,3589],{"className":3585},[1900],[1842,3587],{"className":3588,"style":3411},[1904],[1842,3590,2412],{"className":3591,"style":2434},[1909,1913],[1797,3593,3595],{"id":3594},"_3-estimation-methods","3. Estimation methods",[3597,3598,3599,3618],"table",{},[3600,3601,3602],"thead",{},[3603,3604,3605,3609,3612,3615],"tr",{},[3606,3607,3608],"th",{},"Method",[3606,3610,3611],{},"Idea",[3606,3613,3614],{},"Strength",[3606,3616,3617],{},"Limitation",[3619,3620,3621,3636,3650,3664],"tbody",{},[3603,3622,3623,3627,3630,3633],{},[3624,3625,3626],"td",{},"Maximum likelihood",[3624,3628,3629],{},"maximise observation-model probability",[3624,3631,3632],{},"handles censoring\u002Ftruncation coherently",[3624,3634,3635],{},"can be tail-sensitive and numerically unstable",[3603,3637,3638,3641,3644,3647],{},[3624,3639,3640],{},"Method of moments",[3624,3642,3643],{},"match sample and model moments",[3624,3645,3646],{},"simple and interpretable",[3624,3648,3649],{},"high moments unstable for heavy tails",[3603,3651,3652,3655,3658,3661],{},[3624,3653,3654],{},"Quantile matching",[3624,3656,3657],{},"match selected empirical quantiles",[3624,3659,3660],{},"targets decision-relevant regions",[3624,3662,3663],{},"discards other information",[3603,3665,3666,3669,3672,3675],{},[3624,3667,3668],{},"Bayesian inference",[3624,3670,3671],{},"combine likelihood and prior",[3624,3673,3674],{},"propagates parameter uncertainty",[3624,3676,3677],{},"prior and computation must be justified",[1797,3679,3681],{"id":3680},"_4-fit-candidates-then-test-unseen-data","4. Fit candidates, then test unseen data",[1793,3683,3684],{},"The executable example generates a fixed synthetic lognormal sample. It compares Exponential, Gamma, and lognormal fits using training AIC and held-out negative log score.",[3686,3687],"pyodide",{"code64":3688,"layout":3689,"locale":7,"packages":3690,"title":3691},"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","vertical","numpy,pandas,scipy,matplotlib","Candidate severity models: fit versus prediction",[1793,3693,3694],{},"The synthetic generator makes lognormal plausible, but a finite holdout need not rank it first every run. That sampling variation is part of the lesson.",[1797,3696,3698],{"id":3697},"_5-diagnostics-answer-different-questions","5. Diagnostics answer different questions",[3597,3700,3701,3714],{},[3600,3702,3703],{},[3603,3704,3705,3708,3711],{},[3606,3706,3707],{},"Diagnostic",[3606,3709,3710],{},"Good for",[3606,3712,3713],{},"Weakness",[3619,3715,3716,3727,3738,3749,3760,3771,3782],{},[3603,3717,3718,3721,3724],{},[3624,3719,3720],{},"density\u002Fhistogram",[3624,3722,3723],{},"body shape and modes",[3624,3725,3726],{},"hides tail discrepancies",[3603,3728,3729,3732,3735],{},[3624,3730,3731],{},"empirical vs fitted survival",[3624,3733,3734],{},"exceedance probability",[3624,3736,3737],{},"noisy at extremes",[3603,3739,3740,3743,3746],{},[3624,3741,3742],{},"QQ plot",[3624,3744,3745],{},"quantile calibration",[3624,3747,3748],{},"tail points have high variance",[3603,3750,3751,3754,3757],{},[3624,3752,3753],{},"PP\u002FPIT plot",[3624,3755,3756],{},"overall probability calibration",[3624,3758,3759],{},"can visually underweight tail",[3603,3761,3762,3765,3768],{},[3624,3763,3764],{},"mean excess plot",[3624,3766,3767],{},"threshold-tail behaviour",[3624,3769,3770],{},"highly variable at high thresholds",[3603,3772,3773,3776,3779],{},[3624,3774,3775],{},"held-out log score",[3624,3777,3778],{},"predictive distribution",[3624,3780,3781],{},"sensitive to sample split and dependence",[3603,3783,3784,3787,3790],{},[3624,3785,3786],{},"layer-cost backtest",[3624,3788,3789],{},"actual reinsurance decision",[3624,3791,3792],{},"needs adequate attachment-region data",[1793,3794,3795],{},"Use logarithmic survival axes to make tail differences visible.",[1797,3797,3799],{"id":3798},"_6-aic-and-goodness-of-fit-boundaries","6. AIC and goodness-of-fit boundaries",[1793,3801,3802,3803,3833],{},"For a model with ",[1842,3804,3806,3820],{"className":3805},[1845],[1842,3807,3809],{"className":3808},[1849],[1851,3810,3811],{"xmlns":1853},[1855,3812,3813,3818],{},[1858,3814,3815],{},[1864,3816,3817],{},"k",[1889,3819,3817],{"encoding":1891},[1842,3821,3823],{"className":3822,"ariaHidden":1874},[1896],[1842,3824,3826,3829],{"className":3825},[1900],[1842,3827],{"className":3828,"style":2391},[1904],[1842,3830,3817],{"className":3831,"style":3832},[1909,1913],"margin-right:0.0315em;"," estimated parameters,",[1842,3835,3837],{"className":3836},[2099],[1842,3838,3840,3883],{"className":3839},[1845],[1842,3841,3843],{"className":3842},[1849],[1851,3844,3845],{"xmlns":1853,"display":2108},[1855,3846,3847,3880],{},[1858,3848,3849,3852,3854,3856,3859,3861,3863,3865,3867,3869,3876,3878],{},[1864,3850,3851],{"mathvariant":2115},"AIC",[1872,3853,2148],{},[1872,3855,2125],{},[1868,3857,3858],{},"2",[1864,3860,3817],{},[1872,3862,3396],{},[1868,3864,3858],{},[1864,3866,2116],{"mathvariant":2115},[1872,3868,2046],{"stretchy":2045},[2534,3870,3871,3873],{"accent":1874},[1864,3872,2054],{},[1872,3874,3875],{"stretchy":1874},"^",[1872,3877,2057],{"stretchy":2045},[1864,3879,2167],{"mathvariant":2115},[1889,3881,3882],{"encoding":1891},"\\operatorname{AIC}=2k-2\\ell(\\widehat\\theta).",[1842,3884,3886,3908,3930],{"className":3885,"ariaHidden":1874},[1896],[1842,3887,3889,3892,3899,3902,3905],{"className":3888},[1900],[1842,3890],{"className":3891,"style":3411},[1904],[1842,3893,3895],{"className":3894},[2213],[1842,3896,3851],{"className":3897},[1909,3898],"mathrm",[1842,3900],{"className":3901,"style":2195},[1971],[1842,3903,2125],{"className":3904},[2199],[1842,3906],{"className":3907,"style":2195},[1971],[1842,3909,3911,3915,3918,3921,3924,3927],{"className":3910},[1900],[1842,3912],{"className":3913,"style":3914},[1904],"height:0.7778em;vertical-align:-0.0833em;",[1842,3916,3858],{"className":3917},[1909],[1842,3919,3817],{"className":3920,"style":3832},[1909,1913],[1842,3922],{"className":3923,"style":3415},[1971],[1842,3925,3396],{"className":3926},[3441],[1842,3928],{"className":3929,"style":3415},[1971],[1842,3931,3933,3937,3940,3943,3946,3990,3993],{"className":3932},[1900],[1842,3934],{"className":3935,"style":3936},[1904],"height:1.1844em;vertical-align:-0.25em;",[1842,3938,3858],{"className":3939},[1909],[1842,3941,2116],{"className":3942},[1909],[1842,3944,2046],{"className":3945},[2078],[1842,3947,3949],{"className":3948},[1909,2815],[1842,3950,3952],{"className":3951},[1921],[1842,3953,3955],{"className":3954},[1926],[1842,3956,3959,3967],{"className":3957,"style":3958},[1930],"height:0.9344em;",[1842,3960,3961,3964],{"style":2828},[1842,3962],{"className":3963,"style":2608},[1938],[1842,3965,2054],{"className":3966,"style":2091},[1909,1913],[1842,3968,3972,3975],{"className":3969,"style":3971},[3970],"svg-align","width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6944em;",[1842,3973],{"className":3974,"style":2608},[1938],[1842,3976,3978],{"style":3977},"height:0.24em;",[3979,3980,3986],"svg",{"xmlns":3981,"width":3982,"height":3983,"viewBox":3984,"preserveAspectRatio":3985},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[3987,3988],"path",{"d":3989},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[1842,3991,2057],{"className":3992},[2095],[1842,3994,2167],{"className":3995},[1909],[1793,3997,3998,3999,4002],{},"Lower AIC compares estimated information loss ",[1830,4000,4001],{},"among models fitted to the same observations and likelihood basis",". It is not an absolute fit certificate, and AIC values from differently truncated samples are not directly comparable.",[1793,4004,4005],{},"The ordinary one-sample Kolmogorov–Smirnov null distribution assumes the reference distribution is fully specified. If parameters are fitted from the same data, textbook p-values are generally invalid. Use an appropriate correction or parametric bootstrap:",[1805,4007,4008,4011,4014,4017,4020],{},[1808,4009,4010],{},"fit the model and calculate the observed statistic;",[1808,4012,4013],{},"simulate many samples from the fitted model;",[1808,4015,4016],{},"refit the model to each sample;",[1808,4018,4019],{},"recompute the statistic;",[1808,4021,4022],{},"compare the observed statistic with this simulated reference distribution.",[1797,4024,4026],{"id":4025},"_7-parameter-and-model-uncertainty","7. Parameter and model uncertainty",[1793,4028,4029,4030,4122],{},"A fitted 99.5% quantile ",[1842,4031,4033,4063],{"className":4032},[1845],[1842,4034,4036],{"className":4035},[1849],[1851,4037,4038],{"xmlns":1853},[1855,4039,4040,4060],{},[1858,4041,4042,4045,4047,4050,4052,4058],{},[1864,4043,4044],{},"Q",[1872,4046,2046],{"stretchy":2045},[1868,4048,4049],{},".995",[1872,4051,2051],{"separator":1874},[2534,4053,4054,4056],{"accent":1874},[1864,4055,2054],{},[1872,4057,3875],{"stretchy":1874},[1872,4059,2057],{"stretchy":2045},[1889,4061,4062],{"encoding":1891},"Q(.995;\\widehat\\theta)",[1842,4064,4066],{"className":4065,"ariaHidden":1874},[1896],[1842,4067,4069,4072,4075,4078,4081,4084,4087,4119],{"className":4068},[1900],[1842,4070],{"className":4071,"style":3936},[1904],[1842,4073,4044],{"className":4074},[1909,1913],[1842,4076,2046],{"className":4077},[2078],[1842,4079,4049],{"className":4080},[1909],[1842,4082,2051],{"className":4083},[1967],[1842,4085],{"className":4086,"style":1972},[1971],[1842,4088,4090],{"className":4089},[1909,2815],[1842,4091,4093],{"className":4092},[1921],[1842,4094,4096],{"className":4095},[1926],[1842,4097,4099,4107],{"className":4098,"style":3958},[1930],[1842,4100,4101,4104],{"style":2828},[1842,4102],{"className":4103,"style":2608},[1938],[1842,4105,2054],{"className":4106,"style":2091},[1909,1913],[1842,4108,4110,4113],{"className":4109,"style":3971},[3970],[1842,4111],{"className":4112,"style":2608},[1938],[1842,4114,4115],{"style":3977},[3979,4116,4117],{"xmlns":3981,"width":3982,"height":3983,"viewBox":3984,"preserveAspectRatio":3985},[3987,4118],{"d":3989},[1842,4120,2057],{"className":4121},[2095]," is a point estimate. Quantify uncertainty with profile likelihood, bootstrap, posterior draws, and\u002For alternative plausible families. For a high layer, model spread can dominate sampling error within one chosen family.",[1797,4124,4126],{"id":4125},"practice","Practice",[1805,4128,4129,4132,4135],{},[1808,4130,4131],{},"A dataset records only claims above £10,000. Which likelihood adjustment is required?",[1808,4133,4134],{},"A policy pays £100,000 for every ground-up claim at or above its limit. Is £100,000 an exact ground-up loss?",[1808,4136,4137],{},"Why should a time-dependent portfolio use a chronological holdout rather than a random split?",[4139,4140,4142],"legacy-details",{"title":4141},"Answers",[1805,4143,4144,4225,4228],{},[1808,4145,4146,4147,2167],{},"Left truncation: divide each exact density by ",[1842,4148,4150,4175],{"className":4149},[1845],[1842,4151,4153],{"className":4152},[1849],[1851,4154,4155],{"xmlns":1853},[1855,4156,4157,4172],{},[1858,4158,4159,4161,4163,4165,4167,4170],{},[1864,4160,2496],{},[1872,4162,2046],{"stretchy":2045},[1864,4164,2412],{},[1872,4166,2415],{},[1868,4168,4169],{},"10,000",[1872,4171,2057],{"stretchy":2045},[1889,4173,4174],{"encoding":1891},"P(X>10{,}000)",[1842,4176,4178,4202],{"className":4177,"ariaHidden":1874},[1896],[1842,4179,4181,4184,4187,4190,4193,4196,4199],{"className":4180},[1900],[1842,4182],{"className":4183,"style":2070},[1904],[1842,4185,2496],{"className":4186,"style":2618},[1909,1913],[1842,4188,2046],{"className":4189},[2078],[1842,4191,2412],{"className":4192,"style":2434},[1909,1913],[1842,4194],{"className":4195,"style":2195},[1971],[1842,4197,2415],{"className":4198},[2199],[1842,4200],{"className":4201,"style":2195},[1971],[1842,4203,4205,4208,4212,4218,4222],{"className":4204},[1900],[1842,4206],{"className":4207,"style":2070},[1904],[1842,4209,4211],{"className":4210},[1909],"10",[1842,4213,4215],{"className":4214},[1909],[1842,4216,1875],{"className":4217},[1967],[1842,4219,4221],{"className":4220},[1909],"000",[1842,4223,2057],{"className":4224},[2095],[1808,4226,4227],{},"No. It is a right-censored observation: ground-up loss is known only to be at least £100,000.",[1808,4229,4230],{},"A random split leaks future regimes across train and test; a chronological split better represents prospective prediction under drift.",{"title":10,"searchDepth":4232,"depth":4232,"links":4233},2,[4234,4235,4243,4244,4245,4246,4247,4248],{"id":1799,"depth":4232,"text":1800},{"id":1836,"depth":4232,"text":1837,"children":4236},[4237,4240,4242],{"id":2363,"depth":4238,"text":4239},3,"Left truncation at threshold ddd",{"id":3032,"depth":4238,"text":4241},"Right censoring at limit uuu",{"id":3370,"depth":4238,"text":3371},{"id":3594,"depth":4232,"text":3595},{"id":3680,"depth":4232,"text":3681},{"id":3697,"depth":4232,"text":3698},{"id":3798,"depth":4232,"text":3799},{"id":4025,"depth":4232,"text":4026},{"id":4125,"depth":4232,"text":4126},"Fit the likelihood that generated the observations, then validate the decision-relevant centre and tail.","md",{"sidebar":4252},{"order":4253},4,true,{"title":876,"description":4249},"K-FovcveD8115GiUyKgEplBnv2tJDFZHgWKwqFJkXyU",[4258,4260],{"title":872,"path":873,"stem":874,"description":4259,"children":-1},"Model claim frequency with exposure, overdispersion, heterogeneity, and excess zeros.",{"title":880,"path":881,"stem":882,"description":4261,"children":-1},"Represent distinct risk populations and latent states without mistaking flexibility for explanation.",1785754735021]