Estimation of P(Y < X) for the three-parameter generalized exponential distribution

Mohammad Z. Raqab, Mohamed T. Madi, Debasis Kundu

    Research output: Contribution to journalArticlepeer-review

    105 Citations (Scopus)


    This article considers the estimation of R = P(Y < X) when X and Y are distributed as two independent three-parameter generalized exponential (GE) random variables with different shape parameters but having the same location and scale parameters. A modified maximum likelihood method and a Bayesian technique are used to estimate R on the basis of independent complete samples. The Bayes estimator cannot be obtained in explicit form, and therefore it has been determined using an importance sampling procedure. An analysis of a real life data set is presented for illustrative purposes.

    Original languageEnglish
    Pages (from-to)2854-2864
    Number of pages11
    JournalCommunications in Statistics - Theory and Methods
    Issue number18
    Publication statusPublished - Jan 2008


    • Bayesian estimation
    • Bootstrap confidence intervals
    • Generalized exponential distribution
    • HPD intervals
    • Importance sampling
    • Maximum likelihood estimation

    ASJC Scopus subject areas

    • Statistics and Probability


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