A Comparison of Some Claim Number Distributions

Specialeforsvar ved Sophie Kjær-Hansen

Titel:  A Comparison of Some Claim Number Distributions

Abstract: The aim of this thesis is to compare different claim number distributions. The Generalized Linear Model (GLM) framework is considered as it has some nice properties which we can apply. We consider the Poisson, Negative Binomial and Generalized Poisson regression model, where the two former fit under the GLM framework. It is discussed that the two latter models assume overdispersion which is expected to describe data better. These models are estimated using iterative re-weighted squared methods. The zero-inflated Poisson and zero-inflated Negative Binomial regression models are introduced. These permit a different type of overdispersion originated from the binary part of the models. In order to estimate these models the EM algorithm is used. Hypothesis testing is conducted on the models in order to see which are preferred. Some of examples are considered assume the parameter of interest lies on the boundary of the parameters space where a 50:50 mixture chi-squared distribution is used. Methods and techniques presented are performed on simulated data in order the see how well they perform. Lastly, the models are fitted to shipping data in order to see which claim number distribution is favored. Our results shows that the Negative Binomial model is best suited to describe data 

Vejleder:  Jostein Paulsen
Censor:    Mette M.Havning