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

Author

Listed:
  • 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 .)

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.

Suggested Citation

  • Choudhury Mriganka Mouli & Bhattacharya Rahul & Maiti Sudhansu S., 2022. "Estimation of P(X ≤ Y) for discrete distributions with non-identical support," Statistics in Transition New Series, Polish Statistical Association, vol. 23(3), pages 43-64, September.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:3:p:43-64:n:8
    DOI: 10.2478/stattrans-2022-0029
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