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Empirical Bayes estimation of the guarantee lifetime in a two-parameter exponential distribution

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  • Huang, Wen-Tao
  • Huang, Hui-Hsin

Abstract

We study empirical Bayes estimation of the guarantee lifetime [theta] in a two-parameter exponential distribution having a probability density p(x[theta],[beta])=(1/[beta])exp(-(x-[theta])/[beta])I(x-[theta]) with unknown scale parameter [beta]. An empirical Bayes estimator is proposed and its associated asymptotic optimality is studied. It is shown that is asymptotically optimal in the sense that its regret converges to zero at a rate n-2r/(2r+1), where n is the number of past observations available and r is a positive integer related to the prior distribution G.

Suggested Citation

  • Huang, Wen-Tao & Huang, Hui-Hsin, 2006. "Empirical Bayes estimation of the guarantee lifetime in a two-parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1821-1829, October.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:16:p:1821-1829
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    References listed on IDEAS

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    1. Li Jianjun & Gupta Shanti S., 2001. "Monotone Empirical Bayes Tests With Optimal Rate Of Convergence For A Truncation Parameter," Statistics & Risk Modeling, De Gruyter, vol. 19(3), pages 223-238, March.
    2. Liang, TaChen, 1993. "Convergence rates for empirical Bayes estimation of the scale parameter in a Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 35-45, June.
    3. Tiwari, Ram C. & Zalkikar, Jyoti N., 1990. "Empirical Bayes estimation of the scale parameter in a Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 261-270, December.
    4. Li, Jianjun & S. Gupta, Shanti, 2003. "Optimal rate of empirical Bayes tests for lower truncation parameters," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 177-185, November.
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    Cited by:

    1. Lee-Shen Chen, 2009. "On empirical Bayes two-tail tests for double exponential distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 1037-1049.
    2. Wang, Lichun & Singh, Radhey S., 2014. "Linear Bayes estimator for the two-parameter exponential family under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 633-642.
    3. Takatoshi Sugiyama & Toru Ogura, 2022. "Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-40, March.

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