Estimation of R = P [Y < X ] for Three Parameter Generalized Rayleigh Distribution

نویسندگان

  • Debasis Kundu
  • Mohammad Z. Raqab
چکیده

Surles and Padgett [15] introduced two-parameter Burr Type X distribution, which can be described as a generalized Rayleigh distribution. In this paper we consider the estimation of the stress-strength parameter R = P [Y < X], when X and Y are both three-parameter generalized Rayleigh distribution with the same scale and locations parameters but different shape parameters. It is assumed that they are independently distributed. It is observed that the maximum likelihood estimators (MLEs) do not exist, and we propose a modified maximum likelihood estimator of R. We obtain the asymptotic distribution of the modified maximum likelihood estimator of R and it can be used to construct the asymptotic confidence interval of R. We also propose the Bayes estimate of R and the construction of the associated credible interval based on importance sampling technique. Analysis of two real data sets, (i) simulated and (ii) real, have been performed for illustrative purposes.

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تاریخ انتشار 2013