Common distributions in general Insurance

This section provides a comprehensive overview of the probability distributions commonly employed in actuarial practice. We will examine their key properties, explore their applications in insurance contexts, and discuss methodologies for fitting these distributions to empirical data.

Distributions for Modeling Claim Severity (Losses)

In the first part of this section, we will focus on the distributions that govern claim amounts or the claim losses. These distributions are used to model the severity of individual claims and are essential for pricing insurance policies and setting reserves.

The following distributions are commonly used to model claim severity:

• The exponential distribution
• The gamma distribution
• The lognormal distribution

All details about these distributions can be found in the Loss Distribution section.

Distributions for Modeling Claim Frequency

In the second part of this section, we will discuss the distributions used to model the frequency of claims. These distributions govern the number of claims that occur over a given period and are crucial for pricing insurance policies and assessing risk. We will explore two common distributions for cases:

• Pareto distribution
• Weibull distribution

You can access the details of these distributions in the Claim Frequency section.

Fitting distributions to data

After we have discussed the common distributions for claim amounts and cases, we will explore how to fit these distributions to real-world data.

Fitting distributions to data is a crucial step in the actuarial analysis process, as it allows us to estimate the parameters of the distribution and assess its goodness of fit.

We will discuss the methods for fitting distributions to data and explore the statistical techniques used to evaluate the fit of a distribution with the following methods:

• Kolmogorov-Smirnov test
• Chi-square goodness-of-fit test