Estimation of the Reliability Characteristics by Using Classical and Bayesian Methods of Estimation for the Mgamma Distribution

ABSTRACT

In this article, we discuss the estimation of reliability characteristics for the Mgamma lifetime distribution, specifically the reliability function and the mean time to system failure. First, using comprehensive numerical simulations, four distinct frequentist estimation techniques for these reliability measures at a given time are shown and contrasted according to their mean squared errors. Second, the standard, percentile, and bias‐corrected percentile bootstrap confidence intervals (BCIs) are assessed. Third, for the suggested model, Bayesian estimation is performed with a gamma prior under three distinct loss functions. Fourth, we derive the highest posterior density (HPD) credible intervals for both the reliability function as well as mean time to system failure. The average widths and coverage probabilities of the HPD intervals and the classical bootstrap confidence intervals) BCIs are compared through a Monte Carlo simulation study. Lastly, a real data set is examined to demonstrate the applicability of the suggested techniques.