Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Abstract

This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations.

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

“…Additionally, Kotb and Raqab [16] explored Bayesian estimation of model parameters and prediction of unobserved data from the Rayleigh distribution using RSS. Furthermore, Ren et al [17] examined entropy estimation for a GR distribution within progressively type-II censored samples. Rao [18] estimated R in a multi-component system using the maximum likelihood method of estimation in samples drawn from a generalized Rayleigh distribution.…”