Actuarial Modelling of Claim Counts
Risk Classification, Credibility and Bonus-Malus Systems
Chapter One
Mixed Poisson Models for Claim
Numbers
1.1 Introduction
1.1.1 Poisson Modelling for the Number of Claims
In view of the economic importance of motor third party liability insurance in industrialized
countries, many attempts have been made in the actuarial literature to find a probabilistic
model for the distribution of the number of claims reported by insured drivers. This chapter
aims to introduce the basic probability models for count data that will be applied in motor
insurance. References to alternative models are gathered in the closing section to this chapter.
The Binomial distribution is the discrete probability distribution of the number of successes
in a sequence of n independent yes/no experiments, each of which yields success with
probability q. Such a success/failure experiment is also called a Bernoulli experiment or
Bernoulli trial. Two important distributions arise as approxim ... read full excerpt from Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems ebook
