Loss Distributions and Modeling

Parametric loss models, severity and frequency distributions, and aggregate claims.

Key Concepts

• •Severity distributions: exponential, Pareto, lognormal, Weibull, and gamma
• •Frequency distributions: Poisson, negative binomial, and binomial
• •Coverage modifications: deductibles, limits, coinsurance, and inflation adjustments
• •Limited expected values: E[min(X, d)] and their role in coverage pricing
• •Aggregate loss models: compound distributions and collective risk models
• •Maximum likelihood estimation for fitting distributions to loss data
• •Truncated and censored data: adjusting estimation for incomplete observations
• •Mixture and spliced distributions: modeling heterogeneous loss populations
• •Heavy-tailed distributions: Pareto, log-Pareto, and their tail behavior
• •Goodness-of-fit: chi-squared test, KS test, and QQ plots for distribution selection

Study Tips

• 1.Memorize the pdf, cdf, mean, and variance for each key distribution.
• 2.Practice problems with deductibles and limits until the formulas are automatic.
• 3.Understand how truncation and censoring affect the likelihood function.
• 4.Work through aggregate loss model problems using both exact and approximate methods.
• 5.Use QQ plots to build intuition about which distribution fits a given dataset.

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