BAYES SHRINKAGE ESTIMATION OF RELIABILITY AND THE PARAMETERS OF A FINITE-RANGE FAILURE TIME MODEL

A finite range failure time distribution has been proposed and studied. For estimating the two parameters of this distribution, this paper considers a prior assumption that (1 - b) is the probability that the scale parameter theta and shape parameter p have the values theta0 and p0, respectively, and that the rest of the probability mass b(0 less-than-or-equal-to b less-than-or-equal-to 1) is distributed as h(p, theta) = h1(p)h2(theta). The value h1(p) is a uniform density for p and h2(theta) is an inverted gamma density for theta. With this prior density, Bayes estimators are first obtained and then Bayesian shrinkage estimators are defined. Bayesian shrinkage estimators are compared with maximum likelihood estimators (m.l.e.) and it was found that the proposed estimators are better than m.l.e. for quite a wide range of parameters.