Statistical Inference on the Entropy Measures of Gamma Distribution under Progressive Censoring: EM and MCMC Algorithms

Studying the ages of mobile phones is considered one of the most important things in the recent period in the field of shopping and modern technology. In this paper, we will consider that the ages of these phones follow a gamma distribution under progressive first-failure (PFF) censoring. All of the unknown parameters, as well as Shannon and Rényi entropies, were estimated for this distribution. The maximum likelihood (ML) approach was utilized to generate point estimates for the target parameters based on the considered censoring strategy. The asymptotic confidence intervals of the ML estimators (MLEs) of the targeted parameters were produced using the normal approximation to ML and log-transformed ML. We employed the delta method to approximate the variances of the Shannon and Rényi functions to obtain their asymptotic confidence intervals. Additionally, all parameter estimates utilized in this study were determined using the successful expectation–maximization (EM) method. The Metropolis–Hastings (MH) algorithm was applied to construct the Bayes estimators and related highest posterior density (HPD) credible intervals under various loss functions. Further, the proposed methodologies were contrasted using Monte Carlo simulations. Finally, the radio transceiver dataset was analyzed to substantiate our results.