Counting Processes
Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot · Wiley series in probability and statistics · 2013
This chapter focuses on the analysis of probability distributions of random variables, such as the amount of a claim, or the number of claims over a fixed period of time. For analyzing risk, the distribution of the number of claims may not be sufficient. The chapter examines counting processes that are Markovian and further restrict attention to a particular type of counting process called a nonhomogeneous birth process. The mixed Poisson distribution was motivated as a model to address heterogeneity within the population. Mixing has a natural extension to the counting process formulation and allows for observation of the development of claims over time. Controlled Vocabulary Terms Poisson distribution; probability