On the Parameter of the Burr Type X under Bayesian Principles

Authors: T. N. Sindhu, M. Aslam

Abstract:

A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.

Keywords: Credible Intervals, Loss Functions, Posterior Predictive Distributions, Predictive Intervals.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091264

References:

[1] I. W. Burr, "Cumulative Frequency Distribution,” Annals of Mathematical Statistics, vol. 13, pp. 215-232, 1942.
[2] J.G. Surles and W.J. Padgett, "Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution,” Lifetime Data Analysis, vol. 7, pp. 187-200, 2001.
[3] H.A. Sartawi and M.S. Abu-Salih, "Bayes Prediction Bounds for the Burr Type X Model,” Communications in Statistics - Theory and Methods, vol. 20, pp. 2307-2330, 1991.
[4] Z.F. Jaheen, "Empirical Bayes Estimation of the Reliability and Failure Rate Functions of the Burr Type X Failure Model,” Journal of Applied Statistical Sciences, vol. 3, pp. 281-288, 1996.
[5] K.E. Ahmad, M.E. Fakhry, and Z.F. Jaheen, "Empirical Bayes Estimation of P(Y < X) and Characterization of Burr-Type X Model,” Journal of Statistical Planning and Inference, vol. 64, pp. 297-308, 1997.
[6] M.Z. Raqab, "Order Statistics from the Burr Type X Model,” Computers Mathematics and Applications, vol. 36, pp. 111-120, 1998.
[7] M. Saleem, M. Aslam, "On Bayesian Analysis of the Rayleigh Survival Times under Assuming the Rayleigh Censor Time,” Pak. J. of Statistics, vol. 25, pp. 71-82, 2009.
[8] S. D. Grimshaw, B. J. Collings, W. A. Larsen, and C. R. Hurt, "Eliciting Factor Importance in a Designed Experiment,” Technometrics, vol. 43, pp. 133-146, 2001.
[9] A. O'Hagan, C. E. Buck, A. Daneshkhah, A. Eiser, P. H. Garthwaite, D. J. Jenkinson, J. E. Oakley, and T. Rakow, "Uncertain Judgements: Eliciting Expert Probabilities,” John Wiley & Sons, 2006.
[10] D. Jenkinson, "The Elicitation of Probabilities: A Review of the Statistical Literature,” Department of Probability and Statistics, University of Sheffield, 2005.
[11] J. C. Leon, J. F. Vazquez-Polo, and L.R. Gonzalez, "Environmental and Resource Economics,” Kluwer Academic Publishers, vol. 26, pp. 199-210, 2003.
[12] M. Aslam, "An Application of Prior Predictive Distribution to Elicit the Prior Density,” Journal of Statistical Theory and Applications, vol. 2, pp. 70-83, 2003.
[13] A. K. Bansal, "Bayesian Parametric Inference,” Norsa Publishing House, New Delhi.