Bayesian Inference on Residual Tsallis Entropy of the Inverse Weibull Model: A Progressive Type I Censoring Approach

Abstract

Lately, there has been a great deal of interest in the process of measuring uncertainty about probability distributions. Shannon (1948) introduced the Shannon entropy measure to the field of information theory. Based on Ebrahimi (1996), the residual version of entropy functions is introduced. Throughout this work, the estimation of residual Tsallis (RT) entropy for the inverse Weibull (IW) distribution under the progressive Censoring Type-I approach is discussed. Non-Bayesian and Bayesian inference methods are used to estimate the RT entropy of the IW distribution. The RT Bayesian estimators are evaluated under non-informative and informative priors based on linear exponential loss functions and squared error. A Monto Carlo simulation study and an illustration using actual data sets were conducted to assess the estimators' performance. From simulated outcomes, RT maximum likelihood and Bayesian estimators under progressive censoring Type-I perform well as the sample size grows. Additionally, Bayesian estimators of RT entropy measure under the LINEX-II loss function are superior to other competing estimators.