Bayesian Estimation of Entropy for Kumaraswamy Distribution and Its Application to Progressively First-Failure Censored Data

Entropy can be mathematically defined as a measure of the uncertainty of random variables that represents the potential quantity of information. This article investigates the behavior of the entropy of random variables which follow a Kumaraswamy distribution using progressively first-failure censored (PFFC) data. In particular, we calculate the maximum likelihood estimation and the confidence interval of entropy by using the observed Fisher information matrix through the asymptotic distribution of the maximum likelihood estimator. Furthermore, we apply the Markov Chain Monte Carlo (MCMC) method which help us to estimates the entropy and to formulation the credible intervals in order to address this problem. Here, a numerical example of real data is presented to illustrate the performance of the proposed method. Finally, we perform Monte Carlo simulations to observe the behavior of the proposed procedure.