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Estimation after selection from exponential populations with unequal scale parameters

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  • Mohd. Arshad

    (Indian Institute of Technology Kanpur
    Aligarh Muslim University)

  • Neeraj Misra

    (Indian Institute of Technology Kanpur)

Abstract

Consider $$k$$ k ( $$\ge $$ ≥ 2) exponential populations having unknown guarantee times and known (possibly unequal) failure rates. For selecting the unknown population having the largest guarantee time, with samples of (possibly) unequal sizes from the $$k$$ k populations, we consider a class of selection rules based on natural estimators of the guarantee times. We deal with the problem of estimating the guarantee time of the population selected, using a fixed selection rule from this class, under the squared error loss function. The uniformly minimum variance unbiased estimator (UMVUE) is derived. We also consider two other natural estimators $$\varphi _{N,1}$$ φ N , 1 and $$\varphi _{N,2}$$ φ N , 2 which are, respectively, based on the maximum likelihood estimators and UMVUEs for component problems. The estimator $$\varphi _{N,2}$$ φ N , 2 is shown to be generalized Bayes. We further show that the UMVUE and the natural estimator $$\varphi _{N,1}$$ φ N , 1 are inadmissible and are dominated by the natural estimator $$\varphi _{N,2}$$ φ N , 2 . A simulation study on the performance of various estimators is also reported.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0670-6
    DOI: 10.1007/s00362-015-0670-6
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    References listed on IDEAS

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    1. P. Vellaisamy & Abraham Punnen, 2002. "Improved estimators for the selected location parameters," Statistical Papers, Springer, vol. 43(2), pages 291-299, April.
    2. 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.
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    Cited by:

    1. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2021. "Minimax estimation of the common variance and precision of two normal populations with ordered restricted means," Statistical Papers, Springer, vol. 62(1), pages 209-233, February.
    2. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.

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