Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data

Abstract

Based on joint progressive Type-II censored data, we examined the statistical inference of the generalized logistic distribution with different shape and scale parameters in this research. Wherever possible, we explored maximum likelihood estimators for unknown parameters within the scope of the joint progressive censoring scheme. Bayesian inferences for these parameters were demonstrated using a Gamma prior under the squared error loss function and the linear exponential loss function. It was important to note that obtaining Bayes estimators and the corresponding credible intervals was not straightforward; thus, we recommended using the Markov Chain Monte Carlo method to compute them. We performed real-world data analysis for demonstrative purposes and ran Monte Carlo simulations to compare the performance of all the suggested approaches.