Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Abstract

Families of distributions are commonly used to model insurance claims data that require flexible distributional forms in a satisfactory manner, but the specification problem to assess the goodness-of-fit of the hypothesized model can sometimes be a challenge due to the complexity of the likelihood function of the family of distributions involved. The previous work shows that these specification problems can be attacked by means of semi-parametric tests based on generalized method of moment (GMM) estimators. While the approach can be directly applied to both discrete and continuous families of distributions, the paper focuses on developing a testing strategy within a framework of discrete families of distributions. Both the local power analysis and the approximate slope method demonstrate the excellent performance of these tests. The finite-sample performance of the tests, based on both asymptotic and bootstrap critical values, are also discussed and are compared with established methods that require the complete specification of likelihood functions.