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 θ and shape parameter p have the values θ₀ and p₀, respectively, and that the rest of the probability mass b(0 ≤ b ≤ 1) is distributed as h(p,θ) = h₁(p)h₂(θ). The value h₁(p) is a uniform density for p and h₂(θ) is an inverted gamma density for θ. 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.