Estimating the Entropy for Lomax Distribution Based on Generalized Progressively Hybrid Censoring

Shuhan Liu,Wenhao Gui

doi:10.3390/sym11101219

Abstract

As it is often unavoidable to obtain incomplete data in life testing and survival analysis, research on censoring data is becoming increasingly popular. In this paper, the problem of estimating the entropy of a two-parameter Lomax distribution based on generalized progressively hybrid censoring is considered. The maximum likelihood estimators of the unknown parameters are derived to estimate the entropy. Further, Bayesian estimates are computed under symmetric and asymmetric loss functions, including squared error, linex, and general entropy loss function. As we cannot obtain analytical Bayesian estimates directly, the Lindley method and the Tierney and Kadane method are applied. A simulation study is conducted and a real data set is analyzed for illustrative purposes.

Highlights

Lomax distribution, conditionally known as Pareto Type II distribution, is a heavy tail distribution widely used in reliability analysis, life testing problems, information theory, business, economics, queuing problems, actuarial modeling and biological sciences
Using Equation (18), the Bayesian estimates under squared error loss function can be obtained as: ĤS
The problem of estimating the entropy for Lomax distribution is considered in this paper, based on generalized progressively hybrid censoring

Summary

Introduction

Conditionally known as Pareto Type II distribution, is a heavy tail distribution widely used in reliability analysis, life testing problems, information theory, business, economics, queuing problems, actuarial modeling and biological sciences. Afaq [3] derived the Bayesian estimators of Lomax distribution under three different loss functions using Jeffery’s and an extension of Jeffery’s prior, and compared the Bayesian estimates with the maximum likelihood estimate by using mean squared error. Ismail [4] derived the maximum likelihood estimators and interval estimators of the unknown parameters under a step-stress model supposing that the time to failure has a Lomax distribution with failure-censoring and studied the optimal test designs

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Conclusion