ON BAYES PREDICTION OF FUTURE MEDIAN

Abstract

An expression for the Bayesian predictive survival function of the median of a set of future observations is obtained whether its size is assumed to be odd or even. Both of the informative and future samples are drawn from a population whose distribution is a general class that includes several distributions used in life testing (and other areas as well) such as the Weibull (including the exponential and Rayleigh), compound Weibull (including the compound exponential and compound Rayleigh), Pareto, beta, Gompertz and compound Gompertz, among other distributions. A general proper (conjugate) prior density function is used to cover most prior distributions that have been used in literature. Applications to the Weibull, exponential and Rayleigh models are illustrated.