Statistical Inference Based on Censored Data of Entropy for Lomax Distribution

The current research centers around entropy. This paper investigates the estimation of entropy for the Lomax (Lo) distribution using an adaptive progressive Type-II censored data. The entropy maximum likelihood estimate is computed and the bootstrap confidence intervals of entropy are displayed, approximate confidence intervals are constructed using the asymptotic normality of maximum likelihood estimation and the observed Fisher information matrix. The Bayes entropy estimator is demonstrated using the symmetric and asymmetric loss functions. To further assess the performance of the entropy estimators, particularly under various loss functions, such as linear exponential and squared error, the posterior distribution was calculated. Then, using Monte Carlo simulations, various approaches are compared to identify the believable intervals of the entropy's highest posterior density. Lastly, the recommended methods are illustrated using a numerical example.