Special Issue 2022 – Call for Papers
A New Role for Statistics: The Joint Special Issue of "Statistics in Transition New Series" (SiTns) and "Statystyka Ukraïny" (SU)
Mriganka Mouli Choudhury https://orcid.org/0000-0003-1686-6389 , Rahul Bhattacharya https://orcid.org/0000-0002-3748-717X , Sudhansu S. Maiti https://orcid.org/0000-0001-8906-6513

© M. M. Choudhury, R. Bhattacharya, S. S. Maiti. Article available under the CC BY-SA 4.0 licence

ARTICLE

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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

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