Estimation of Entropy for Weibull Distribution Based on Record Values

Manoj Chacko,P S Asha

doi:10.2991/jsta.d.210610.001

Abstract

In this paper, estimation of entropy for Weibull distribution based on record values is considered. Maximum likelihood estimation and Bayes estimation for Shannon entropy and Renyi entropy have been considered based on record values. Bayes estimators are obtained using Markov Chain Monte Carlo (MCMC) method. A simulation study is performed to find the performance of the estimators developed in this paper. The inferential procedures developed in this paper have also been illustrated using real data.

Highlights

Let {Xi, i ≥ 1} be a sequence of independent and identically distributed random variables having an absolutely continuous cumulative distribution function F(x) and probability density function f (x)
In a number of situations, only observations that exceed or only those that fall below the current extreme value are recorded
By invariant property of maximum likelihood estimators (MLEs), the MLE of Shannon entropy for Weibull distribution based on upper record values is given by MLE of Renyi entropy for Weibull distribution based on upper record values is given by

Summary

INTRODUCTION

Let {Xi, i ≥ 1} be a sequence of independent and identically distributed (iid) random variables having an absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f (x). Seo et al [9] developed an entropy estimation method for upper record values from the generalized halflogistic distribution. Chacko and Asha [15] considered the problem of estimation of entropy for generalized exponential distribution using lower record values. If the observations available are only in the form of record values and the parent population follows Weibull distribution the inferential procedure developed in this work can be utilized to estimate the entropies of the system or process. Cho et al [19] obtained estimators for the entropy function of a Weibull distribution based on generalized Type II hybrid censored samples. We consider the estimation of entropies for Weibull distribution based on upper record values.

MAXIMUM LIKELIHOOD ESTIMATION

BAYESIAN ESTIMATION

MCMC Method

SIMULATION STUDY

ILLUSTRATION USING REAL DATA

Findings

CONCLUSION