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

• Authors: Mriganka Mouli Choudhury , Rahul Bhattacharya , Sudhansu S. Maiti

Abstracts

EN

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

EN

stress-strength model; uniformly minimum variance unbiased; maximum likelihood

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2022
• Volume: 23
• Issue: 3
• Pages: 43-64

Dates

published

2022

Contributors

author

Mriganka Mouli Choudhury

• Visva-Bharati University, Department of Statistics

• https://orcid.org/0000000316866389

author

Rahul Bhattacharya

• University of Calcutta, Department of Statistics

• https://orcid.org/000000023748717X

author

Sudhansu S. Maiti

• Visva-Bharati University, Department of Statistics

• https://orcid.org/0000000189066513

References

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Identifiers

DOI

10.2478/stattrans-2022-0029

Biblioteka Nauki

2107147