Abstract
In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study.
Highlights
In the last decade, finite mixture models have emerged as flexible models due to their applications in applied sciences, engineering, and physical sciences
The mixture models can be used in a situation when the data are presented in the form of the overall mixture models. e overall mixture models are called the direct application of the mixture models, and their applications can be seen in medicine, botany, zoology, agriculture, economics, life testing, reliability, and survival analysis. e various aspects of mixture models were discussed by Li and Sedransk [3]. e interested readers can refer the work of Harris [4], Kanji [5], and Jones and McLachlan [6] on the application of mixture models for reallife problems
Inspired by the wide real-life applications of mixture distributions, the main objective of this study is to develop a new three-component mixture of Pareto distributions (TCMPD) for lifetime data modeling under type I mixture
Summary
Finite mixture models have emerged as flexible models due to their applications in applied sciences, engineering, and physical sciences. Most of the researchers have comprehensively applied mixture distributions in various real-life situations and estimated parameters using the Bayesian and classical methods. Mathematical Problems in Engineering discussed situations where data are assumed to follow a three-component mixture of suitable probability distributions [22,23,24,25,26,27,28]. With the application of mixture modeling, estimates of the proportions of various minerals in the sand can be obtained. Inspired by the wide real-life applications of mixture distributions, the main objective of this study is to develop a new three-component mixture of Pareto distributions (TCMPD) for lifetime data modeling under type I mixture. · 1 − w1e− λ1 ln y − w2e− λ2 ln y − 1 − w1 − w2e− λ3 ln y
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