On counting distributions related to the Delaporte distribution

Katarzyna Steliga ¹   ; Dominik Szynal ²

¹ Department of Mathematics Lublin University of Technology Nadbystrzycka 38A 20-618 Lublin, Poland
² Institute of Mathematics Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1 20-031 Lublin, Poland

Applicationes Mathematicae, Tome 46 (2019) no. 1, pp. 1-38

Résumé

We introduce the $\alpha $-modified negative binomial distribution and the $\alpha $-modified Delaporte distribution. The Delaporte distribution is a member of the class of $\alpha $-modified Delaporte distributions. The probability distributions studied can be applied e.g. in actuarial sciences. The main result of the paper shows that the $\alpha $-modified negative binomial distribution fits the number of automobile insurance claims better than the negative binomial distribution, while the $\alpha $-modified Delaporte distribution describes the number of car accidents better than the classical Delaporte distribution. Characteristics of the distributions considered (moments, coefficient of variation, skewness and kurtosis) are computed. Moreover, we study some compounds of the $\alpha $-modified negative binomial and $\alpha $-modified Delaporte distributions. We also study the compound $\alpha $-modified Delaporte distribution with Borel summands and gamma summands. Characteristics (moments, coefficient of variation, skewness and kurtosis) of these distributions are computed. Moreover, the compound $\alpha $-modified negative binomial distribution with gamma summands is investigated.

Détail

DOI : 10.4064/am2337-8-2018

Keywords: introduce alpha modified negative binomial distribution alpha modified delaporte distribution delaporte distribution member class alpha modified delaporte distributions probability distributions studied applied actuarial sciences main result paper shows alpha modified negative binomial distribution fits number automobile insurance claims better negative binomial distribution while alpha modified delaporte distribution describes number car accidents better classical delaporte distribution characteristics distributions considered moments coefficient variation skewness kurtosis computed moreover study compounds alpha modified negative binomial alpha modified delaporte distributions study compound alpha modified delaporte distribution borel summands gamma summands characteristics moments coefficient variation skewness kurtosis these distributions computed moreover compound alpha modified negative binomial distribution gamma summands investigated