Shifting Shape-Parameter in Life Tests: A Bayes Analysis

A problem related to prediction of an order statistic in a future sample based on earlier samples is analysed here. The basis for this analysis is a predictive distribution. The problem is that, during a life test while sampling, the shape parameter shifts from an exponential to a gamma. Under this situation, the effects on the Bayes prediction region and on the variance of the predictive distribution are analysed. The discussion includes change in prior degree of belief as well.