Paremeter Estimation and Prediction of the Exponential Life Time Model via Bayesian Approach

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Paremeter Estimation and Prediction of the Exponential Life Time Model via Bayesian Approach

Author Affiliations

¹Department of Statistics, University of Peshawar, Peshawar, PAKISTAN
²Department of Statistics, Government Post Graduate College of Science, Faisalabad, PAKISTAN

Res. J. Recent Sci., Volume 4, Issue (10), Pages 25-31, October,2 (2015)

Abstract

In this paper the Bayesian analysis for Exponential model assuming uninformative conjugate (Jeffrey’s and Uniform) and informative conjugate (inverted gamma and two component inverted gamma mixture) priors is presented. The comparison between the two approaches is made on the basis of Bayes estimates, posterior risks, credible intervals and highest posterior density regions for different sample sizes and parameter values. The Bayesian predictive intervals assuming informative priors are calculated for different combinations of the hyperparameters to discover the range of hyper-parameters that lead towards more precise estimates of the parameters of interest.

References

Sinha S.K., Bayesian Estimation, New Age International (P) Limited, New Delhi, (1998)
Javed M. and Saleem M Alamgir, A Bayesian Analysis of the Rayleigh Life Time Model, World Applied Science Journal, 16(2), 220-226 (2012)
Sinha S.K. and Howlader H.A., Credible and HPD intervals of the parameter and reliability of Rayleigh distribution, IEEE Transactions-Reliability, 32, 217-220 (1983)
Lalitha S. and Mishra A., Modified maximum likelihood estimation for Rayleigh distribution, Communications in Statistics: Theory and Methods, 25, 389-401 (1996)
Bose S., Bayesian robustness with mixture classes of priors, The Annals of Statistics, 22(2), 652-667 (1994)
Bolstad W.M., Introduction to Bayesian Statistics. John Wiley and Sons Inc. New Jersey (2004)
Mendenhall W. and Hader R.A., Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data, Biometrika, 45(3-4), 504-520 (1958)
Dey Sanku and Das M.K., A note on prediction interval for a Rayleigh distribution: Bayesian approach, In the proceedings of International Workshop/ Conference on Bayesian Statistics and its Applications Banaras Hindu University, Varanasi, India (2005)
Saleem M. and Aslam M., On Prior Selection for the Mixture of Rayleigh Distribution using Predictive Intervals, Pakistan Journal of Statistics, 24(1), 21-35 (2008)
Saleem M., Aslam M. and Economou P., On the Bayesian analysis of the mixture of Power function distribution using the complete and the censored sample, Journal of Applied Statistics, 37(1), 25-40 (2010)

[ref1] Sinha S.K., Bayesian Estimation, New Age International (P) Limited, New Delhi, (1998)

[ref2] Javed M. and Saleem M Alamgir, A Bayesian Analysis of the Rayleigh Life Time Model, World Applied Science Journal, 16(2), 220-226 (2012)

[ref3] Sinha S.K. and Howlader H.A., Credible and HPD intervals of the parameter and reliability of Rayleigh distribution, IEEE Transactions-Reliability, 32, 217-220 (1983)

[ref4] Lalitha S. and Mishra A., Modified maximum likelihood estimation for Rayleigh distribution, Communications in Statistics: Theory and Methods, 25, 389-401 (1996)

[ref5] Bose S., Bayesian robustness with mixture classes of priors, The Annals of Statistics, 22(2), 652-667 (1994)

[ref6] Bolstad W.M., Introduction to Bayesian Statistics. John Wiley and Sons Inc. New Jersey (2004)

[ref7] Mendenhall W. and Hader R.A., Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data, Biometrika, 45(3-4), 504-520 (1958)

[ref8] Dey Sanku and Das M.K., A note on prediction interval for a Rayleigh distribution: Bayesian approach, In the proceedings of International Workshop/ Conference on Bayesian Statistics and its Applications Banaras Hindu University, Varanasi, India (2005)

[ref9] Saleem M. and Aslam M., On Prior Selection for the Mixture of Rayleigh Distribution using Predictive Intervals, Pakistan Journal of Statistics, 24(1), 21-35 (2008)

[ref10] Saleem M., Aslam M. and Economou P., On the Bayesian analysis of the mixture of Power function distribution using the complete and the censored sample, Journal of Applied Statistics, 37(1), 25-40 (2010)