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Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation

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  • M. E. Ghitany
  • W. H. Laverty

Abstract

In this paper we discuss the behavlor of the statistic R ^ ( t ) , the uniformly minimum variance unbiased (UMVU) estimate for the reliability of gamma distribution with unknown scale parameter σ when an outlier observation is present. Given the outlier effect on σ , we determine bounds for the mean and mean square error (MSE) of R(t). A semi-Bayesian approach is discussed when the outlier effect on σ is treated as a random variable having a prior distribution of beta type. Results of the exponential distribution (Sinha [1]) are given as particular cases of our results.

Suggested Citation

  • M. E. Ghitany & W. H. Laverty, 1989. "Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:376741
    DOI: 10.1155/S0161171289000980
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