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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 797-804
http://dx.doi.org/10.1155/S0161171289000980

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

Department of Mathematics, University of Saskatchewan, Saskatoon S7N OWO, Saskatchewan, Canada

Received 6 August 1987; Revised 5 December 1988

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.