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Estimating the parameter of the population selected from discrete exponential family

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  • Vellaisamy, P.
  • Jain, Sushmita

Abstract

Let X1,...,Xp be p independent random observations, where Xi is from the ith discrete population with density of the form ui([theta]i)ti(xi)[theta]ixi, where [theta]i is the positive unknown parameter. Let X(1)=...=X(l)>X(l+1)>=...>=X(m)>X(m+1)=...=X(p) denote the ordered observations, where the ordering is done from the largest to the smallest and from smaller index to larger ones, among equal observations. Suppose the population corresponding to X(1) (or X(m+1)) is selected, and [theta](i) denotes the parameter associated with . In this paper, we consider the estimation of [theta](1) (or [theta](m+1)) under the loss Lk(t,[theta])=(t-[theta])2/[theta]k, for k>=0, an integer. We construct explicit estimators, specifically for the cases k=0 and k=1, of [theta](1) and [theta](m+1) that dominate the natural estimators, by solving certain difference inequalities. In particular, improved estimators for the selected Poisson and negative binomial distributions are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1076-1087
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    References listed on IDEAS

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    1. Neeraj Misra & Edward Meulen, 2003. "On estimating the mean of the selected normal population under the LINEX loss function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 173-183, September.
    2. 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. 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.
    2. Mohammadi, Zohreh & Towhidi, Mina, 2017. "Estimating the parameters of a selected bivariate normal population," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 205-210.
    3. Liang, TaChen, 2009. "Comments on "Estimating the parameter of the population selected from discrete exponential family"," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2208-2211, October.
    4. 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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