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Discrete uniform and binomial distributions with infinite support

Pepelyshev, Andrey and Zhigljavsky, Anatoly 2020. Discrete uniform and binomial distributions with infinite support. Soft Computing 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: Published Online
Status: In Press
Schools: Mathematics
Publisher: Springer
ISSN: 1432-7643
Date of First Compliant Deposit: 22 July 2020
Date of Acceptance: 1 July 2020
Last Modified: 27 Jul 2020 08:44
URI: http://orca.cf.ac.uk/id/eprint/133626

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