International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 797-804
doi: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 M. E. Ghitany and W. H. Laverty. 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.