Estimation and Prediction for an Exponential Form Distribution Based on Combined Type-II Censored Samples

A. R. Shafay1,2, N. Balakrishnan3
1Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
2Nature Science Department, Community College of Riyadh, King Saud University, Riyadh, Saudi Arabia
3Department of Mathematics and Statistics, McMaster University, Hamilton, Canada

Tóm tắt

In this paper, based on combined Type-II censored samples, an exponential form for the underlaying distributions is considered for estimating the unknown parameters using the maximum likelihood and Bayesian methods. Three loss functions are used to derive the Bayesian estimators. Also, the Bayesian prediction for the order statistics from a future sample is calculated. Moreover, the results of the exponential and Pareto distributions are presented as illustrative examples. Finally, for illustrating all the inferential methods discussed in this paper, Monte Carlo simulation and data analysis for the exponential distribution are presented.

Từ khóa


Tài liệu tham khảo

Abdel-Aty, Y., Franz, J., Mahmoud, M.A.W.: Bayesian prediction based on generalized order statistics using multiply type-II censoring. Statistics 41, 495–504 (2007)

Abdel-Aty, Y., Shafay, A.R., Mohie El-Din, M.M., Nagy, M.: Bayesian inference for the inverse exponential distribution based on pooled Type-II censored samples. J Stat. Appl. Probab. 4, 239–246 (2015)

AL-Hussaini, E.K.: Predicting observables from a general class of distributions. J. Stat. Plan. Inference 79, 79–91 (1999)

Al-Hussaini, E.K., Ahmed, A.A.: On Bayesian predictive distributions of generalized order statistics. Metrika 57, 165–176 (2003)

AL-Hussaini, E.K., Al-Awadhi, F.: Bayes two-sample prediction of generalized order statistics with fixed and random sample size. J. Stat. Comput. Simul. 80, 13–28 (2010)

Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. Wiley, New York (1992)

Arnold, B.C., Press, S.J.: Bayesian estimation and prediction for Pareto data. J. Am. Stat. Assoc. 84, 1079–1084 (1989)

Balakrishnan, N.: Progressive censoring methodology: an appraisal. Test 16, 211–296 (2007). (with discussions)

Balakrishnan, N., Aggarwala, R.: Progressive Censoring: Theory. Methods and Applications. Birkhäuser, Boston (2000)

Balakrishnan, N., Beutner, E., Cramer, E.: Exact two-sample non-parametric confidence, prediction, and tolerance intervals based on ordinary and progressively Type-II right censored data. Test 19, 68–91 (2010)

Balakrishnan, N., Cramer, E.: Computational aspects of statistical intervals based on two Type-II censored samples. Comput. Stat. 28, 893–917 (2013)

Balakrishnan, N., Shafay, A.R.: One- and two-sample bayesian prediction intervals based on Type-II hybrid censored data. Commun. Stat. Theory Methods 41, 1511–1531 (2012)

Basu, A.P., Ebrahimi, N.: Bayesian approach to life testing and reliability estimation using asymmetric loss function. J. Stat. Plan. Inference 29, 21–31 (1991)

Dey, D.K., Ghosh, M., Srinivasan, C.: Simultaneous estimation of parameters under entropy loss. J. Stat. Plan. Inference 15, 347–363 (1987)

Lwin, T.: Estimation of the tail of the Paretian law. Skand. Aktuarietidskr. 55, 170–178 (1972)

Mohie El-Din, M.M., Abdel-Aty, Y., Shafay, A.R.: Two-sample Bayesian prediction intervals of generalized order statistics based on multiply Type II censored data. Commun. Stat. Theory Methods 41, 381–392 (2012)

Mohie El-Din, M.M., Shafay, A.R.: One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data. Stat. Pap. 54, 287–307 (2013)

Nassar, M.M., Eissa, F.H.: Bayesian estimation for the exponentiated Weibull model. Commun. Stat. Theory Methods 33, 2343–2362 (2004)

Nelson, W.: Applied Life Data Analysis. Wiley, New York (1982)

Pandey, B.N.: Estimator of the scale parameter of the exponential distribution using LINEX loss function. Commun. Stat. Theory Methods 26, 2191–2202 (1997)

Rojo, J.: On the admissibility of \(c \overline{X}+d\) with respect to the LINEX loss function. Commun. Stat. Theory Methods 16, 3745–3748 (1987)

Shafay, A.R., Balakrishnan, N.: One- and two-sample Bayesian prediction intervals based on Type-I hybrid censored data. Commun. Stat. Simul. Comput. 41, 65–88 (2012)

Soliman, A.A.: Reliability estimation in a generalized life-model with application to the Burr-XII. IEEE Trans. Reliab. 51, 337–343 (2002)

Soliman, A.A.: Estimation of parameters of life from progressively censored data using Burr XII model. IEEE Trans. Reliab. 54, 34–42 (2005)

Soliman, A.A., Abd Ellah, A.H., Sultan, K.S.: Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches. Comput. Stat. Data Anal. 51, 2065–2077 (2006)

Varian, H.R.: A Bayesian Approach to Real Estate Assessment. North-Holland, Amsterdam (1975)

Volterman, W., Balakrishnan, N.: Exact nonparametric confidence, prediction and tolerance intervals based on multi-sample Type-II right censored data. J. Stat. Plan. Inference 140, 3306–3316 (2010)

Volterman, W., Balakrishnan, N., Cramer, E.: Exact nonparametric meta-analysis for multiple independent doubly Type-II censored samples. Comput. Stat. Data Anal. 56, 1243–1255 (2012)