Generalized Poisson random variable: its distributional properties and actuarial applications

被引:0
|
作者
Faroughi, Pouya [1 ,2 ]
Li, Shu [1 ]
Ren, Jiandong [1 ]
机构
[1] Western Univ, Dept Stat & Actuarial Sci, London, ON, Canada
[2] Univ Prince Edward Isl, Sch Math & Computat Sci, Charlottetown, PE, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Generalized Poisson distribution; generalized negative binomial distribution; compound random variables; moment transforms; recursive formulas; risk measures;
D O I
10.1017/S1748499524000198
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
Generalized Poisson (GP) distribution was introduced in Consul & Jain ((1973). Technometrics, 15(4), 791-799.). Since then it has found various applications in actuarial science and other areas. In this paper, we focus on the distributional properties of GP and its related distributions. In particular, we study the distributional properties of distributions in the $\mathcal{H}$ family, which includes GP and generalized negative binomial distributions as special cases. We demonstrate that the moment and size-biased transformations of distributions within the $\mathcal{H}$ family remain in the same family, which significantly extends the results presented in Ambagaspitiya & Balakrishnan ((1994). ASTINBulletin: the Journal of the IAA, 24(2), 255-263.) and Ambagaspitiya ((1995). Insurance Mathematics and Economics, 2(16), 107-127.). Such findings enable us to provide recursive formulas for evaluating risk measures, such as Value-at-Risk and conditional tail expectation of the compound GP distributions. In addition, we show that the risk measures can be calculated by making use of transform methods, such as fast Fourier transform. In fact, the transformation method showed a remarkable time advantage over the recursive method. We numerically compare the risk measures of the compound sums when the primary distributions are Poisson and GP. The results illustrate the model risk for the loss frequency distribution.
引用
收藏
页数:19
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