ESTIMATING THE FINITE POPULATION VERSIONS OF MEAN RESIDUAL LIFE-TIME FUNCTION AND HAZARD FUNCTION USING BAYES METHOD

NADER EBRAHIMI

Division of Statistics, Northern Illinois University, DeKalb, IL 60115-2854, U.S.A.

(Received March 27, 1996; revised April 23, 1997)

Abstract. In this paper we introduce a finite population version of the mean residual life-time (MRL) function and the hazard function, and study Bayesian estimation of these functions. The unknown parameter is the complete set (y_{1}, …, y_{N}) of lifetimes of the N units which constitute the complete population. A hierarchical type prior is used, where the y_{i}’s are assumed conditionally independent given a random parameter θ. The data consists of a random sample of n values of y_{i}. The Bayes estimators of MRL and hazard functions, respectively, are then obtained as the posterior expectations of the unknown functions.

Key words and phrases: Finite population, mean residual life-time function, hazard function, exponential distribution, prior distribution, posterior distribution, exchangeability, type I censoring, type II censoring.