Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior

Ammara Nawaz Cheema,Ibrahim M Almanjahie,Muhammad Aslam,Ishfaq Ahmad

doi:10.1155/2020/8765321

Abstract

Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

Highlights

Mixture modeling exists in many situations, whenever we have more than one subpopulation
Two symmetric and two asymmetric loss functions (LFs) are used with noninformative priors, uniform prior (UP), and Jeffreys prior (JP), to obtain such results. e estimators are derived by applying the type I right censoring scheme
Bayes estimators (BEs) and PRs under LFs. e real-valued function which illustrates a loss for estimator over the exact value of parameter is defined as loss function (LF). e current section discussed BEs and posterior risks (PRs) over four different LFs, that is, squared error loss function (SELF), quadratic loss function (QLF), precautionary loss function (PLF), and DeGroot loss function (DLF)

Summary

Introduction

Mixture modeling exists in many situations, whenever we have more than one subpopulation. Bayesian analysis of shape parameter of EIWD under different loss functions (LFs) is discussed in [6]. The authors in [9] studied 3-component mixture model of Pareto distribution by using type I right censoring scheme. E authors in [11] explored 3-component mixture of Mathematical Problems in Engineering exponential distribution under different loss functions. The authors in [12] performed Bayesian estimation for finite mixture of exponential, Rayleigh, and Burr type XII distribution. E main focus of this paper is to highlight efficient Bayes estimators (BEs) of component and proportional parameter(s) For this reason, two symmetric and two asymmetric LFs are used with noninformative priors, uniform prior (UP), and Jeffreys prior (JP), to obtain such results.

The 3-Component Mixture of the EIWD

Limiting Expressions

Simulation Study

Practical Application

Conclusion