风险理论中的计数分布

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2021-01-01 DOI:10.56082/annalsarscimath.2022.1-2.20

K. Kostadinova, M. Lazarova

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引用次数: 0

摘要

本文介绍了风险理论中一些重要的计数分布。第一个是I-Delaporte分布。它是非中心负二项分布的一般化。第二个分布是非中心P´olya-Aeppli分布。它是两个独立随机变量的和，一个是泊松分布，另一个是P´olya-Aeppli分布。还考虑了P′olya- aeppli - lindley分布、复合P′olya分布和复合二项分布。它们是混合P´olya-Aeppli分布与林德利混合分布、复合负二项分布和复合二项分布与几何复合分布。这些分布的主要应用是它们可以作为风险模型中相应计数过程的分布

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COUNTING DISTRIBUTIONS IN RISK THEORY

In this paper we introduce some signiﬁcant counting distributionsin risk theory. The ﬁrst one is the I-Delaporte distribution. It is ageneralization of the Non-central negative binomial distribution. Thesecond distribution is the Non-central P´olya-Aeppli distribution. It isa sum of two independent random variables, one that is a Poisson andanother one, a P´olya-Aeppli distributed. The P´olya-Aeppli-Lindley,the compound P´olya and compound binomial distributions are alsoconsidered. They are mixed P´olya-Aeppli distribution with Lindleymixing distribution, compound negative binomial and compound bi-nomial distribution with geometric compounding distribution. Themain application of these distributions is that they can be used ascorresponding counting processes’ distributions in risk models

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.