Bayesian Estimation for 3-Component Mixture of Generalized Exponential Distribution

Kazmi, Syed Mohsin Ali; Aslam, Muhammad

doi:10.1007/s40995-018-0625-6

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…Wang et al [ 27 ] discussed the applicability of 2CMGEM in medical sciences. Similarly, Kazmi and Aslam [ 28 ] advocated the employment of GE mixture model to fit various right censored datasets. More recent contributions regarding the analysis of 2CMGEM can be seen from the following works.…”

Section: Introductionmentioning

confidence: 99%

An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health

Feroze

Akgül

Jawa

et al. 2022

Computational and Mathematical Methods in Medicine

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Analysis of environmental data with lower detection limits (LDL) using mixture models has recently gained importance. However, only a particular type of mixture models under classical estimation methods have been used in the literature. We have proposed the Bayesian analysis for the said data using mixture models. In addition, an optimal mixture distribution to model such data has been explored. The sensitivity of the proposed estimators with respect to LDL, model parameters, hyperparameters, mixing weights, loss functions, sample size, and Bayesian estimation methods has also been proposed. The optimal number of components for the mixture has also been explored. As a practical example, we analyzed two environmental datasets involving LDL. We also compared the proposed estimators with existing estimators, based on different goodness of fit criteria. The results under the proposed estimators were more convincing as compared to those using existing estimators.

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Section: Introductionmentioning

confidence: 99%

An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health

Feroze

Akgül

Jawa

et al. 2022

Computational and Mathematical Methods in Medicine

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show abstract

“…Mohamed et al [15] introduced the methodology to obtain the Bayesian predictions using MGED. Kazmi and Aslam [16] considered the Bayesian analysis for right censored using MGED assuming shape parameters to be known. The above discussion sug-gests that the MGED is very relevant distribution in modeling the censored datasets.…”

Section: Introductionmentioning

confidence: 99%

On Suitability of Mixture of Generalized Exponential Models in Modeling Right-Censored Medical Datasets Using Conditional Expectations

Feroze

Akgül

Al-Alwan

et al. 2022

Computational and Mathematical Methods in Medicine

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The exploration of suitable models for modeling censored medical datasets is of great importance. There are numerous studies dealing with modeling the censored medical datasets. However, majority of the earlier contributions have utilized the conventional models for modeling the said datasets. Unfortunately, the conventional models are not capable of capturing the behavior of the heterogeneous datasets involving the mixture of two or more subpopulations. In addition, the earlier contributions have considered conventional censoring schemes by replacing all the censored items with the largest failed item. This paper is aimed at proposing the analysis of right-censored mixture medical datasets. The mixture of the generalized exponential distribution has been proposed to model the right-censored heterogeneous medical datasets. In converse to conventional censoring schemes, we have proposed censoring schemes which replace the censored items with conditional expectation (CE) of the random variable. In addition, the Bayesian methods have been proposed to estimate the model parameters. The performance and sensitivity of the proposed estimators have been evaluated using a detailed simulation study. The detailed simulation study suggests that censoring schemes based on CE provide improved estimation as compared to conventional censoring schemes. The suitability of the model in modeling heterogeneous datasets has been verified by modeling two real right-censored medical datasets. The comparison of the proposed model with existing mixture model under Bayesian methods advocated the improved performance of the proposed model.

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“…On the other hand, the estimation of parameters in Bayesian framework for a mixture of two distributions has been considered by many researchers [10][11][12][13][14][15][16][17][18][19][20][21]. Contrary to the two-component mixture modeling, some authors have discussed situations where data are assumed to follow a three-component mixture of suitable probability distributions [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

Tahir

Almanjahie

Abid

et al. 2021

Mathematical Problems in Engineering

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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.

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Bayesian Estimation for 3-Component Mixture of Generalized Exponential Distribution

Cited by 7 publications

References 25 publications

An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health

An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health

On Suitability of Mixture of Generalized Exponential Models in Modeling Right-Censored Medical Datasets Using Conditional Expectations

On Estimation of Three-Component Mixture of Distributions via Bayesian and Classical Approaches

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