Three-Component Mixture of Rayleigh Model Under Doubly Censored Samples: A Bayesian Look

Abstract

Feroze and Aslam (J Natl Sci Found Sri Lanka 42:325–334, 2014) and Sindhu et al. (J Mod Appl Stat Methods 13:259–286, 2014) have considered the Bayesian analysis of the two-component mixture of lifetime distributions under doubly censored samples. In this paper, the concept has been extended for the three-component mixture of lifetime (Rayleigh) distribution under doubly censored samples. The likelihood function for the mixture of lifetime models under doubly type-II censored samples has been introduced. Different priors and loss functions have been assumed for the derivation of Bayes estimators and posterior risks. The comparisons among various estimators have been made by analyzing the simulated and real data sets.

Keywords

Mixture distributions / Prior elicitation / Posterior distribution / Loss functions

References

[1] Acheson MA, McElwee EM. Concerning the reliability of electron tubes. Sylvania Technol.. 1951, 1951 4

[2] Ali S, Aslam M, Abbas N, Kazmi SMA, Hasan T. On process capability and system availability analysis of the inverse Rayleigh distribution. Pak. J. Stat. Oper. Res.. 2015, 11 1 53-66

[3] Asgharzadeh A, Azizpour M. Bayesian inference for Rayleigh distribution under hybrid censoring. Int. J. Syst. Assur. Eng. Manag.. 2016, 7 3 239-249

[4] Aslam M. An application of prior predictive distribution to elicit the prior density. J. Stat. Theory Appl.. 2003, 2 1 183-197

[5] Aslam M, Tahir M, Hussain Z, Al-Zahrani B. A 3-component mixture of Rayleigh distributions: properties and estimation in Bayesian framework. PLoS One.. 2015, 10 5 e0126183

[6] Dey S, Dey T. Bayesian estimation and prediction intervals for a Rayleigh distribution under a conjugate prior. J. Stat. Comput. Simul.. 2012, 82 11 1651-1660

[7] Dey S, Dey T. Statistical inference for the Rayleigh distribution under progressively type-II censoring with binomial removal. Appl. Math. Model.. 2014, 38 3 974-982

[8] Eluebaly T, Bougila N. Bayesian learning of finite generalized Gaussian mixture models on images. Signal Process.. 2011, 91 4 801-820

[9] Feroze N, Aslam M. Bayesian analysis of doubly censored lifetime data using two component mixture of Weibull distribution. J. Natl. Sci. Found. Sri Lanka. 2014, 42 4 325-334

[10] Feroze N, Sindhu TN, Aslam M, Yasin W. Doubly censored mixture of two Rayleigh distributions: properties and applications. Maejo Int. J. Sci. Technol.. 2015, 9 03 312-327

[11] Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis. 2004 2 New York: Chapman and Hall/CRC

[12] Kalaiselvi S, Loganathan A, Vijayaraghavan R. Bayesian reliability sampling plans under the conditions of Rayleigh-inverse-Rayleigh distribution. Econ. Qual. Control. 2014, 29 1 29-38

[13] Kantam RRL, Sriram B. Some methods of estimation from censored samples in exponential and Nakagami models. J. Mod. Appl. Stat. Methods. 2014, 13 2 324-354

[14] Kundu D, Howlader H. Bayesian inference and prediction of the inverse Weibull distribution for type-II censored data. Comput. Stat. Data Anal.. 2010, 54 6 1547-1558

[15] Lawless JF. Statistical Models and Methods for Lifetime Data. Wiley Series in Probability and Statistics. 2003 2 New York: Wiley. P-573

[16] Liu HB, Yin T, Wang C. E-Bayes estimation of Rayleigh distribution parameter. Appl. Mech. Mater.. 2014, 596 305-308

[17] Saleem M, Aslam M. Bayesian analysis of the two-component mixture of the Rayleigh distribution assuming the uniform and the Jeffreys’ priors. J. Appl. Stat. Sci.. 2008, 16 493-502

[18] Saleem M, Aslam M, Economou P. On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample. J. Appl. Stat.. 2010, 37 1 25-40

[19] Shi Y, Yan W. The EB estimation of scale parameter for two parameter exponential distribution under the type-I censoring life test. J. Phys. Sci.. 2010, 4 25-30

[20] Sindhu TN, Feroze N, Aslam M. Bayesian estimation of the parameters of two component mixture of rayleigh distribution under doubly censoring. J. Mod. Appl. Stat. Methods. 2014, 13 2 259-286

[21] Soliman AA. Estimators for the finite mixture of Rayleigh model based on progressively censored data. Commun. Stat. Theory Methods. 2006, 35 803-820

[22] Sultan KS, Al-Moisheer AS. Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under type-2 censoring. J. Stat. Comput. Simul.. 2012, 83 1-15

[23] Sultan KS, Ismail MA, Al-Moisheer AS. Mixture of two inverse Weibull distributions: properties and estimation. Comput. Stat. Data Anal.. 2007, 51 5377-5387

[24] Yu B. A Bayesian MCMC approach to survival analysis with doubly-censored data. Comput. Stat. Data Anal.. 2010, 54 8 1921-1929