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Maximum Likelihood Estimation for Generalized Pareto Distribution under Progressive Censoring with Binomial Removals
Statistics Department, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
- 1 Statistics Department, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Open Journal of Statistics·Volume 02 (2012)·Pages 420–423·Published 30 October 2012·DOI10.4236/ojs.2012.24051
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Abstract
The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to follow a binomial distribution. Maximum likelihood estimators and the asymptotic variance-covariance matrix of the estimates are obtained. Finally, a numerical example is given to illustrate the obtained results
KeywordsPareto DistributionBinomial RemovalProgressive CensoringMaximum Likelihood Estimator
- A. Balkema and L. de Haan, “Residual Life Time at Great Age,” Annals of Probability, Vol. 2, No. 5, 1974, pp. 792- 804. doi:10.1214/aop/1176996548
- M. C. Bryson, “Heavy-Tailed Distributions: Properties and Tests,” Technometrics, Vol. 16, No. 1, 1974, pp. 61-68. doi:10.1080/00401706.1974.10489150
- N. Johnson, S. Kotz and N. Balakrishnan, “Continuous Univariate Distribution,” Vol. 1, 2nd Edition, John Wiley, New York, 1994.
- B. C. Arnold, “Pareto Distributions,” Silver Spring, International Cooperative Publishing House, Maryland, 1983.
- N. Balakrishnan and R. Aggarwala, “Progressive Censoring: Theory Methods and Applications,” Birkhuser Publishers, Boston, 2000.
- H. K. Yuen and S. K. Tse, “Parameters Estimation for Weibull Distributed Lifetimes under Progressive Censoring with Random Removals,” Journal of Statistical Computation & Simulation, Vol. 55, No. 1, 1996, pp. 57-71. doi:10.1080/00949659608811749
- S. K. Tse and H. K. Yuen, “Expected Experiment Times for the Weibull Distribution under Progressive Censoring with Random Removals,” Journal of Applied Statistics, Vol. 25, No. 1, 1998, pp. 75-83. doi:10.1080/02664769823313
- S. K. Tse, C. Yang and H. K. Yuen, “Statistical Analysis of Weibull Distributed Lifetime Data under Type-II Progressive Censoring with Binomial Removals,” Journal of Applied Statistics, Vol. 27, No. 8, 2000, pp. 1033-1043. doi:10.1080/02664760050173355
- W. Shuo-Jye and C. Chun-Tao, “Inference in the Pareto Distribution Based on Progressive Type II Censoring with Random Removals,” Journal of Applied Statistics, Vol. 30, No. 2, 2003, pp. 163-172. doi:10.1080/0266476022000023721
- S. J. Wu, “Estimation for the Two-Parameter Pareto Distribution under Progressive Censoring with Uniform Removals,” Journal of Statistical Computation and Simulation, Vol. 73, No. 2, 2003, pp. 125-134. doi:10.1080/00949650215732
- S. J. Wu, Y. J. Chen and C. T. Chang, “Statistical Inference Based on Progressively Censored Samples with Random Removals from the Burr Type XII Distribution,” Journal of Statistical Computation and Simulation, Vol. 77, No. 1, 2007, pp. 19-27. doi:10.1080/10629360600569204
- A. C. Cohen, “Progressively Censored Samples in the Life Testing,” Technometrics, Vol. 5, 1963, pp. 327-339. doi:10.1080/00401706.1963.10490102
- R. G. Miller Jr., G. Gong and A. Munoz, “Survival Analysis,” John Wiley and Sons, New York, 1981.