Discrete uniform and binomial distributions with infinite support

Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2020. Discrete uniform and binomial distributions with infinite support. Soft Computing 24 , pp. 17517-17524. 10.1007/s00500-020-05190-2

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Abstract

We study properties of two probability distributions defined on the infinite set {0,1,2,…} and generalizing the ordinary discrete uniform and binomial distributions. Both extensions use the grossone-model of infinity. The first of the two distributions we study is uniform and assigns masses 1/\textcircled1 to all points in the set {0,1,…,\textcircled1−1}, where \textcircled1 denotes the grossone. For this distribution, we study the problem of decomposing a random variable ξ with this distribution as a sum ξ=dξ1+⋯+ξm, where ξ1,…,ξm are independent non-degenerate random variables. Then, we develop an approximation for the probability mass function of the binomial distribution Bin(\textcircled1,p) with p=c/\textcircled1α with 1/2<α≤1. The accuracy of this approximation is assessed using a numerical study.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	1432-7643
Date of First Compliant Deposit:	22 July 2020
Date of Acceptance:	1 July 2020
Last Modified:	07 Nov 2023 01:13
URI:	https://orca.cardiff.ac.uk/id/eprint/133626

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