**Autors:** Lazarova, M. D., Krasimira Yankova Kostadinova.
**Title:** Counting distributions in risk theory
**Keywords:** conting distributions, mixed distributions, compound distributions**Abstract:** In this paper we introduce some significant counting distributions in risk theory. The first one is the I-Delaporte distribution. It is a generalization of the Non-central negative binomial distribution. The second disribution 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 the compound binomial distributions are also considered. They are mixed Polya-Aeppli 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.
**References**
- Kostadinova, K., Lazarova, M., 2021, Counting distributions in risk thoery, Annals of the Academy of Romanian Scientists: Series on Mathematics and its Aplications, Volume 13(1-2), pp. pp. 20-44
**Issue**
| , vol. 13, issue 1, pp. 24, 2021, Romania, Ann. Acad. Rom. Sci. Ser. Math. Appl., ISSN 2066-6594 |
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