Bounds for the mean square error of reliability estimation from gamma distribution in presence of an outlier observation (Q1262674)

Summary: We discuss the behavior of the statistic \(\hat R(t)\), the uniformly minimum variance unbiased estimate for the reliability of gamma distribution with unknown scale parameter \(\sigma\) when an outlier observation is present. Given the outlier effect on \(\sigma\), 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 \(\sigma\) is treated as a random variable having a prior distribution of beta type. Results of the exponential distribution are given as particular cases of our results.