Reliability Estimation in Inverse Pareto Distribution Using Progressively First Failure Censored Data

Abstract

The progressively first failure censored (PFFC) data have become very popular in the past decade due to its usefulness in life testing experiments and in reliability theory. The PFFC data record the number of failures and increase the efficiency of the estimators. The inverse Pareto distribution (IPD) is useful when empirical data suggest a decreasing or upside-down bathtub-shaped failure rate functions. In this article, we consider the classical and Bayesian estimation of the model parameter and the reliability characteristics of the IPD using the PFFC data. The maximum likelihood estimators, asymptotic confidence, and bootstrap confidence intervals are considered in the classical estimation. Under the Bayesian paradigm, Bayes estimators based on non-informative and the gamma informative priors under the squared error loss function using Tierney-Kadane approximation, importance sampling, and Metropolis-Hasting (M-H) algorithm are assessed. In addition, the highest probability density (HPD) intervals based on the M-H algorithm are also constructed. To investigate the efficacy of each of the estimation procedures, numerical computations are performed based on a simulation study. Finally, a real data set is re-analyzed to show the applicability of the IPD model under a censoring scheme.

KEYWORDS AND PHRASES:

• Bootstrap confidence intervals
• Bayesian estimation
• Inverse Pareto distribution
• maximum likelihood estimation
• T-K approximation

Acknowledgment

The authors are very grateful to the Editor-in-Chief and anonymous reviewers for their constructive comments and suggestions that led to significant improvement in the previous versions of the manuscript.