One and two-sample Bayesian prediction intervals based on Type-I hybrid censored for a general class of distribution 1-F(x)=[ah (x)+b]c are obtained. For the illustration of the developed results, the inverse Weibull distribution with two unknown parameters and the inverted exponential distribution are used as examples. Using the importance sampling technique and Markov Chain Monte Carlo (MCMC) to compute the approximation predictive survival functions. Finally, a real life data set and a generated data set are used to illustrate the results derived here.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4) |
| DOI | 10.11648/j.ajtas.20160504.15 |
| Page(s) | 192-201 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Bayesian Prediction, Type-I Hybrid Censored, General Class, Markov Chain Monte Carlo, Importance Sampling Technique
| [1] | Howlader, H. A., 1985. HPD prediction intervals for Rayleigh distribution. IEEE Trans. Reliab. 34, 121–123. |
| [2] | Geisser, S., 1993. Predictive Inference: An Introduction. Chapman & Hall, New York. |
| [3] | Raqab, M. Z. and Nagaraja, H. N., 1995. On some predictors of future order statistic. Metron. 53, 185-204. |
| [4] | Al-Hussaini, E. K. and Jaheen, Z. F., 1995. Bayesian prediction bounds for the Burr type XII model. Commun Stat Theory Methods. 24, 1829-1842. |
| [5] | Al-Hussaini, E. K. and Jaheen, Z. F., 1996. Bayesian prediction bounds for the Burr type XII distribution in the presence of outliers. J Stat Plan Inference. 55, 23-37. |
| [6] | Abdel-Aty, Y.; Franz, J., Mahmoud, M. A. W., 2007. Bayesian prediction based on generalized order statistics using multiply Type II censored. Statistics. 41, 495-504. |
| [7] | Kundu, D. and Howlader, H., 2010. Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. Comput Stat Data Anal. 54, 1547-1558. |
| [8] | Mohie El-Din, M. M., Abdel-Aty, Y. and Shafay, A. R., 2011. Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample. J. of the Egy. Math. Societ. 19, 102−105. |
| [9] | Mohie El-Din, M. M., Abdel-Aty, Y. and Shafay, A. R., 2011. Bayesian prediction for order statistics from a general class of distributions based on left Type-II censored data. Int. j. math. comput. 13, 1−8. |
| [10] | Shafay, A. R. and Balakrishnan, N., 2010. One- and two-sample Bayesian prediction intervals based on Type-I hybrid censored data. Commun Stat Simul Comput. 41, 65-88. |
| [11] | Mohie El-Din, M. M. and Shafay, A. R., 2013. One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data. Stat Pap. 54, 287-307. |
| [12] | Shafay, A. R., Balakrishnan, N. and Abdel-Aty, Y., 2014. Bayesian inference based on a jointly Type-II censored sample from two exponential populations. J Stat Comput Simul 84, 2427-2440. |
| [13] | Khan, A. H. and Abu-Salih, M. S., 1989. Characterization of probability distributions by conditional expectation of order statistics. Metron. 47, 171-181. |
| [14] | Athar, H. and Islam, H., 2004. Recurrence relations for single and product moments of generalized order statistics from a general class of distribution, Metron. LXII, 3, 327-337. |
| [15] | Guure, C. B., Ibrahim, N. A. and Al Omari, A. M., 2012. Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys’ prior information with three loss functions, Math Probl Eng. Article ID 589640, 13 pages. |
| [16] | Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N., 1992. A First Course in Order Statistics. New York: John Wiley & Sons. |
| [17] | Geweke, J., 1989. Bayesian inference in econometrics models using Monte Carlo integration. Econometrica. 57, 1317-1339. |
| [18] | Chen, M.-H. and Shao, Q. M., 1997. On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25, 1563-1594. |
| [19] | Chen, M-H. and Shao, Q. M., 1999. Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Statist. 8(1), 69-92. |
| [20] | Devroye, L., 1984. A simple algorithm for generating random variates with a log-concave density function. Computing. 33, 247-257. |
| [21] | Dumonceaux, R. and Antle, C. E., 1973. Discriminating between the log-normal and Weibull distribution. Technometrics. 15, 923-926. |
| [22] | Maswadah, M., 2003. Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics. J Stat Comput Simul. 73(12), 887-898. |
| [23] | Singh, S. K., Singh, U. and Sharma, V. K., 2013. Bayesian prediction of future observations from inverse Weibull distribution based on Type-II hybrid censored sample. Int. j. adv. stat. probab. 1(2), 32-43. |
APA Style
Amr Sadek. (2016). Bayesian Prediction Based on Type-I Hybrid Censored Data from a General Class of Distributions. American Journal of Theoretical and Applied Statistics, 5(4), 192-201. https://doi.org/10.11648/j.ajtas.20160504.15
ACS Style
Amr Sadek. Bayesian Prediction Based on Type-I Hybrid Censored Data from a General Class of Distributions. Am. J. Theor. Appl. Stat. 2016, 5(4), 192-201. doi: 10.11648/j.ajtas.20160504.15
AMA Style
Amr Sadek. Bayesian Prediction Based on Type-I Hybrid Censored Data from a General Class of Distributions. Am J Theor Appl Stat. 2016;5(4):192-201. doi: 10.11648/j.ajtas.20160504.15
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Download@article{10.11648/j.ajtas.20160504.15,
author = {Amr Sadek},
title = {Bayesian Prediction Based on Type-I Hybrid Censored Data from a General Class of Distributions},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {5},
number = {4},
pages = {192-201},
doi = {10.11648/j.ajtas.20160504.15},
url = {https://doi.org/10.11648/j.ajtas.20160504.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.15},
abstract = {One and two-sample Bayesian prediction intervals based on Type-I hybrid censored for a general class of distribution 1-F(x)=[ah (x)+b]c are obtained. For the illustration of the developed results, the inverse Weibull distribution with two unknown parameters and the inverted exponential distribution are used as examples. Using the importance sampling technique and Markov Chain Monte Carlo (MCMC) to compute the approximation predictive survival functions. Finally, a real life data set and a generated data set are used to illustrate the results derived here.},
year = {2016}
}
TY - JOUR T1 - Bayesian Prediction Based on Type-I Hybrid Censored Data from a General Class of Distributions AU - Amr Sadek Y1 - 2016/06/14 PY - 2016 N1 - https://doi.org/10.11648/j.ajtas.20160504.15 DO - 10.11648/j.ajtas.20160504.15 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 192 EP - 201 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20160504.15 AB - One and two-sample Bayesian prediction intervals based on Type-I hybrid censored for a general class of distribution 1-F(x)=[ah (x)+b]c are obtained. For the illustration of the developed results, the inverse Weibull distribution with two unknown parameters and the inverted exponential distribution are used as examples. Using the importance sampling technique and Markov Chain Monte Carlo (MCMC) to compute the approximation predictive survival functions. Finally, a real life data set and a generated data set are used to illustrate the results derived here. VL - 5 IS - 4 ER -
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