Estimating Reliability Characteristics of the Log-Logistic Distribution Under Progressive Censoring with Two Applications

Abstract

Let a progressively type-II (PT-II) censored sample of size m is available. Under this set-up, we consider the problem of estimating unknown model parameters and two reliability characteristics of the log-logistic distribution. Maximum likelihood estimates (MLEs) are obtained. We use expectation–maximization (EM) algorithm. The observed Fisher information matrix is computed. We propose Bayes estimates with respect to various loss functions. In this purpose, we adopt Lindley’s approximation and importance sampling methods. Asymptotic and bootstrap confidence intervals are derived. Asymptotic intervals are obtained using two approaches: normal approximation to MLEs and log-transformed MLEs. The bootstrap intervals are computed using boot-t and boot-p algorithms. Further, highest posterior density (HPD) credible intervals are constructed. Two sets of practical data are analyzed for the illustration purpose. Finally, detailed simulation study is carried out to observe the performance of the proposed methods.