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ESTIMATING THE FINITE POPULATION VERSIONS OF

MEAN RESIDUAL LIFE-TIME FUNCTION AND

HAZARD FUNCTION USING BAYES METHOD

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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 *theta*. 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.

**Source**
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