Statistical Inference Based on Censored Data of Entropy for Lomax Distribution

Abstract

^{The current research centers around entropy, which is officially defined as an indicator of the possible amount of information of the Lomax (Lo) distribution that quantifies the uncertainty of random variables. When the parameters are unknown under adaptive progressive Using type-II censored data, the entropy maximum likelihood estimate (MLE) is computed and the bootstrap confidence intervals of entropy is displayed. The Bayes estimator of entropy is demonstrated using both the symmetric and asymmetric loss functions. In the meantime, the posterior is also computed to assess how well the entropy estimators perform in relation to various loss functions. The Bayesian estimates were obtained in a numerical simulation applying the method of Markov Chain Monte Carlo (MCMC). Then, using Monte Carlo simulations, various approaches are compared to identify the believable intervals of the entropy's highest posterior density (HPD). Lastly, the recommended methods are illustrated using a numerical example.}