On counting distributions related to the Delaporte distribution

Volume 46 / 2019

Katarzyna Steliga, Dominik Szynal Applicationes Mathematicae 46 (2019), 1-38 MSC: Primary 60E10; Secondary 62E99. DOI: 10.4064/am2337-8-2018 Published online: 1 February 2019


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.


  • Katarzyna SteligaDepartment of Mathematics
    Lublin University of Technology
    Nadbystrzycka 38A
    20-618 Lublin, Poland
  • Dominik SzynalInstitute of Mathematics
    Maria Curie-Skłodowska University
    pl. M. Curie-Skłodowskiej 1
    20-031 Lublin, Poland

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