Krasimira Y. Kostadinova†, Meglena D. Lazarovav†
Abstract: In this paper we introduce some signi cant counting distributions in risk theory. The rst one is the I-Delaporte distribution. It is a generalization of the Non-central negative binomial distribution. The second distribution is the Non-central Polya-Aeppli distribution. It is a sum of two independent random variables, one that is a Poisson and another one, a Polya-Aeppli distributed. The Polya-Aeppli-Lindley, the compound Polya and compound binomial distributions are also considered. They are mixed Polya-Aeppli distribution with Lindley mixing distribution, compound negative binomial and compound binomial distribution with geometric compounding distribution. The main application of these distributions is that they can be used as corresponding counting processes distributions in risk models.
MSC: 60K10; 62P05.
keywords: counting distributions, mixed distributions, compound distributions
DOI 10.56082/annalsarscimath.2021.1-2.20
†kostadinova@shu.bg Konstantin Preslavsky University of Shumen, Faculty of Mathematics and Informatics, 115, Universitetska St, 9700 Shumen, Bulgaria
meglena.laz@tu-sofia.bg Technical University of So a, Faculty of Applied Mathematics and Informatics, 8, St. Kliment Ohridski Blvd., 1756 So a, Bulgaria
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 13 no 1-2, 2021
