Mixture Modeling of Exponentiated Pareto Distribution in Bayesian Framework With Applications of Wind-Speed and Tensile Strength of Carbon Fiber

Abstract

Mixture modelling has stunning applications to explain the composite problems in simple way. Bayesian demonstration of 3-Component mixture model of Exponentiated Pareto distribution in right-type-I censoring scheme is presented in this article. The posterior densities of the parameter(s) are attained supposing the non-informative (uniform, Jeffreys) priors. The symmetric and asymmetric Loss Functions (Squared Error, Precautionary, Quadratic and DeGroot Loss Function) are assumed to get the Bayes estimator(s) and posterior risk(s). The presentation of the Bayes estimator(s) over posterior risk(s) in the studied loss functions is examined over simulation practice. Two real-data sets, wind speed and tensile strength of carbon fiber, are also analyzed for mixture to complete the performance of Bayes estimator(s). To enhance the study, the limiting forms are also derived for Bayes estimator(s) and posterior risk(s). The results reveal that for the component parameter(s), the Bayes Estimator(s) have their risks accordingly: DeGroot Loss Function < Precautionary Loss Function < Squared Error Loss Function < Quadratic Loss Function, and whereas for the proportion parameter(s) these are classified as: Squared Error Loss Function < Precautionary Loss Function < DeGroot Loss Function < Quadratic Loss Function. Therefore, in this study, DeGroot Loss Function performs efficient and the most preferable non-informative prior is the Jefferys prior for estimation of 3-Component mixture of Pareto distribution.