Reliability analysis of 3-component mixture of distributions

Aslam, Muhammad; Tahir, Muḥammad; Hussain, Zawar

doi:10.24200/sci.2017.4441

Cited by 4 publications

(4 citation statements)

References 29 publications

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“…Ateya and Al Khald [14] studied the finite mixture of truncated generalized Cauchy distribution based on type-I, type-II, and progressively type-II censored samples. Aslam et al [15] studied the threecomponent mixture of exponential, Rayleigh, Pareto, and Burr type-XII distributions in relation to reliability analysis. Tahir et al [16] studied the properties of the three-component mixture of Rayleigh distributions based on doubly censored lifetime data.…”

Section: Introductionmentioning

confidence: 99%

The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

Alotaibi

Khalifa

Baharith

et al. 2021

Mathematical Problems in Engineering

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To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets.

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Section: Introductionmentioning

confidence: 99%

The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

Alotaibi

Khalifa

Baharith

et al. 2021

Mathematical Problems in Engineering

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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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“…Sindhu et al [14] studied the two-component mixture of inverse Weibull distributions under doubly censored sample using various loss functions. Aslam et al [15,16] and Tahir et al [17] studied the properties of three-component mixture of Rayleigh distributions while Ateya [18] discussed the mixture of generalized exponential distribution. Similarly, Benaicha and Chaker [19] also studied the mixture of the Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

On the Bayesian Analysis of Two-Component Mixture of Transmuted Weibull Distribution

2019

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Transmuted distributions are skewed distributions and recently attracted a great attention of researchers due to their applications in reliability and statistics. In this article, our main focus is on the Bayesian estimation of two-component mixture of the Transmuted Weibull Distribution (TWD) under type-I right censored sampling scheme. In order to estimate the unknown parameters, non-informative and informative priors under Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF) are assumed when computing the posterior estimations. In addition, the Bayesian credible intervals (BCI) are also constructed. A Markov Chain Monte Carlo (MCMC) technique is adopted to generate samples from the posterior distributions and in turn computing different posterior summaries, including Bayes estimates (BEs), posterior risks (PRs) and Bayesian credible intervals (BCI). As an illustration, comparison of these Bayes estimators is made through simulated under different loss functions in terms of their respective posterior risks assuming different sample sizes and censoring rates. Two real-life examples, the first being the survival times of hepatitis B & C patients while the second being the hole diameter of 12 mm and the sheet thickness is 3.15 mm, are also discussed to illustrate the potential application of the proposed methodology.

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Reliability analysis of 3-component mixture of distributions

Cited by 4 publications

References 29 publications

The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

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

On the Bayesian Analysis of Two-Component Mixture of Transmuted Weibull Distribution

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