Compound mixed Poisson distributions I

Abstract

The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. In this paper, comprehensive collections of approximate forms are derived for the compound mixed Poisson distribution. The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science.

Keywords:

• Poisson distribution
• compound mixed Poisson distribution

The authors would like to thank the Associate Editor and the referee for carefully reading the paper and for their help in improving the paper.