Estimation of P(X ≤ Y) for discrete distributions with non-identical support

Choudhury Mriganka Mouli (), Bhattacharya Rahul () and Maiti Sudhansu S. ()
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Choudhury Mriganka Mouli: Department of Statistics, Visva-Bharati University, Santiniketan, - 731 235, West Bengal, India .
Bhattacharya Rahul: Department of Statistics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, - 700019, India .
Maiti Sudhansu S.: Department of Statistics, Visva-Bharati University, Santiniketan, - 731 235, West Bengal, India .

Statistics in Transition New Series, 2022, vol. 23, issue 3, 43-64

Abstract: The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distributions, theoretical expressions of such quantities are derived. Similar expressions are obtained when X and Y interchange their roles and both variables are from the discrete uniform distribution. A simulation study is carried out to compare the estimators numerically. A real application based on demand-supply system data is provided.

Keywords: stress-strength model; uniformly minimum variance unbiased; maximum likelihood (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:23:y:2022:i:3:p:43-64:n:8

DOI: 10.2478/stattrans-2022-0029

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