Abstract

This paper provides an exhaustive statistical inference methodology for the Shanker distribution under progressive Type-II censored data. The maximum likelihood estimation (MLE) methods using Newton-Raphson algorithms in the maxLik package for the Shanker distribution for obtaining estimates of the parameter , reliability function , and hazard function  are also provided. The methods use four different kinds of confidence intervals: asymptotic normal approximation (ACI-NA), log-transformed (ACI-NL), Bayesian credible intervals (BCI), and highest posterior density (HPD) intervals. Bayesian estimation using Metropolis-Hastings Markov chain Monte Carlo (MCMC) simulation with a Gamma(2, 2) prior and a Gamma(0.001, 0.001) prior is also provided. The simulation studies using Monte Carlo simulation for six different progressive Type-II censored data patterns to obtain root mean square error (RMSE), mean absolute bias (MAB), average interval length (AIL), and coverage probability (CP) of estimators are also provided. The proposed methods in this paper have also been validated using the Aarset bathtub failure data and ball bearings data. The method uses bootstrap confidence intervals for additional validation. The simulation studies reveal that both MLE and Bayesian methods produce consistent estimates, with moderate improvements in RMSE using the Gamma(2, 2) prior. The method provides effective means to analysts to obtain accurate estimates in reliability studies using progressive censored data.