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Reliability estimation of the selected exponential populations

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  • Kumar, Somesh
  • Mahapatra, Ajaya Kumar
  • Vellaisamy, P.

Abstract

Let [Pi]1,[Pi]2,...,[Pi]k be k populations with [Pi]i being exponential with an unknown location parameter [mu]i and a common but known scale parameter [sigma], i=1,...,k. Suppose independent random samples are drawn from the populations [Pi]1,[Pi]2,...,[Pi]k. Let {Xi1,Xi2,...,Xin} denote the sample drawn from ith population, i=1,...,k. A subset of the populations with high reliabilities is selected according to Gupta's [Gupta, S.S., 1965. On some multiple decision (Selection and Ranking) rules. Technometrics 7, 225-245] subset selection procedure. We consider the problem of estimating simultaneously the reliability functions of the populations in the selected subset. The uniformly minimum variance unbiased estimator (UMVUE) is derived and its inadmissibility is established. An estimator improving the natural estimator is also obtained by using the differential inequality approach used by Vellaisamy and Punnen [Vellaisamy, P., Punnen, A.P., 2002. Improved estimators for the selected location parameters. Statist. Papers 43, 291-299].

Suggested Citation

  • Kumar, Somesh & Mahapatra, Ajaya Kumar & Vellaisamy, P., 2009. "Reliability estimation of the selected exponential populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1372-1377, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:11:p:1372-1377
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    References listed on IDEAS

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    1. Kumar, Somesh & Kar, Aditi, 2001. "Estimating quantiles of a selected exponential population," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 9-19, March.
    2. P. Vellaisamy & Abraham Punnen, 2002. "Improved estimators for the selected location parameters," Statistical Papers, Springer, vol. 43(2), pages 291-299, April.
    3. Vellaisamy, P. & Jain, Sushmita, 2008. "Estimating the parameter of the population selected from discrete exponential family," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1076-1087, July.
    4. Cohen, Arthur & Sackrowitz, Harold B., 1989. "Two stage conditionally unbiased estimators of the selected mean," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 273-278, August.
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    Cited by:

    1. Morteza Amini & Nader Nematollahi, 2017. "Estimation of the Parameters of a Selected Multivariate Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 13-38, February.
    2. Riyadh Al-mosawi, 2012. "Simultaneous estimation following subset selection of binomial populations," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 59-69, April.
    3. Nader Nematollahi, 2017. "Admissible and minimax estimation of the parameter of the selected Pareto population under squared log error loss function," Statistical Papers, Springer, vol. 58(2), pages 319-339, June.
    4. Mohd. Arshad & Neeraj Misra, 2016. "Estimation after selection from exponential populations with unequal scale parameters," Statistical Papers, Springer, vol. 57(3), pages 605-621, September.
    5. Riyadh Rustam Al-Mosawi & Shahjahan Khan, 2018. "Estimating moments of a selected Pareto population under asymmetric scale invariant loss function," Statistical Papers, Springer, vol. 59(1), pages 183-198, March.

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