Some Properties of the Generalized Stuttering Poisson Distribution and its Applications

TL;DR

This paper explores properties of the generalized Stuttering Poisson Distribution (SPD), shows its applicability to insurance data, and demonstrates that a four-parameter SPD provides better data fitting than traditional distributions.

Contribution

It introduces the generalized SPD by relaxing existing conditions and applies it to auto insurance claim data, showing improved modeling accuracy.

Findings

4-th SPD fits auto insurance claim data better than negative binomial and Poisson distributions.

Some distributions used in insurance are shown to be special cases of SPD.

The paper develops cumulant estimation methods for generalized SPD parameters.

Abstract

Based on the probability generating function of stuttering Poisson distribution (SPD), this paper considers some equivalent propositions of SPD. From this, we show that some distributions in the application of non-life insurance actuarial science are SPD, such as negative binomial distribution, compound Poisson distribution etc.. By weakening condition of equivalent propositions of SPD, we define the generalized SPD. We consider cumulant estimation of generalized SPD's parameters. As an application, we use SPD with four parameters (4-th SPD) to fit auto insurance claim data. The fitting results show that 4-th SPD is more accurate than negative binomial and Poisson distribution.