Goodness-of-Fit Tests for Loss Distributions
Review goodness-of-fit testing methods used to validate loss distribution models on Exam STAM.
Why Goodness-of-Fit Matters
After fitting a parametric distribution to loss data, you must verify the model fits adequately. Goodness-of-fit tests compare observed data to the fitted model's predictions. Common tests include chi-squared, Kolmogorov-Smirnov (KS), and Anderson-Darling (AD). The choice of test depends on data characteristics, sample size, and what aspects of fit matter most. A poor fit may indicate the wrong distributional family, inadequate parameter estimation, or structural issues in the data.
Applying the Tests
The chi-squared test groups data into intervals and compares observed and expected counts. KS uses the maximum absolute difference between empirical and fitted CDFs. Anderson-Darling weights tail differences more heavily, making it more sensitive to tail fit. For Exam STAM, know the test statistics, critical values, and when each test is most appropriate. KS works with ungrouped data, chi-squared requires grouping, and Anderson-Darling is particularly useful when tail accuracy matters for risk management applications.