Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 237940, 7 pages
http://dx.doi.org/10.1155/2013/237940
Research Article

Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals

Department of Statistics, Sardar Patel University, Vallabh Vidyanagar 388120, India

Received 30 October 2012; Accepted 19 November 2012

Academic Editors: B. L. Granovsky and X. Lu

Copyright © 2013 Ashok Shanubhogue and N. R. Jain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Balakrishnan, E. Cramer, U. Kamps, and N. Schenk, “Progressive type II censored order statistics from exponential distributions,” Statistics, vol. 35, no. 4, pp. 537–556, 2001. View at Google Scholar · View at Scopus
  2. M. M. M. El-Din and A. R. Shafay, “One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data,” Statistical Papers. In press. View at Publisher · View at Google Scholar
  3. C. Kim, J. Jung, and Y. Chung, “Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring,” Statistical Papers, vol. 52, no. 1, pp. 53–70, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Kim and K. Han, “Estimation of the scale parameter of the half-logistic distribution under progressively type II censored sample,” Statistical Papers, vol. 51, no. 2, pp. 375–387, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. M. A. M. Ali Mousa and Z. F. Jaheen, “Bayesian prediction for progressively censored data from the Burr model,” Statistical Papers, vol. 43, no. 4, pp. 587–593, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. C. J. Pérez-González and A. J. Fernández, “Accuracy of approximate progressively censored reliability sampling plans for exponential models,” Statistical Papers, vol. 50, no. 1, pp. 161–170, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods and Applications, Birkhauser, Boston, Mass, USA, 2000.
  8. N. Balakrishnan, “Progressive censoring methodology: an appraisal,” Test, vol. 16, no. 2, pp. 211–259, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Gompertz, “On the nature of the function expressive of the law of human mortality and on the new mode of determining the value of life contingencies,” Philosophical Transactions of the Royal Society A, vol. 115, pp. 513–580, 1825. View at Google Scholar
  10. M. M. Ananda, R. J. Dalpatadu, and A. K. Singh, “Adaptive bayes estimators for parameters of the Gompertz survival model,” Applied Mathematics and Computation, vol. 75, no. 2-3, pp. 167–177, 1996. View at Google Scholar · View at Scopus
  11. S. G. Walker and S. A. Adham, “A multivariate Gompertz-type distribution,” Journal of Applied Statistics, vol. 28, pp. 1051–1065, 2001. View at Google Scholar
  12. Z. F. Jaheen, “A Bayesian analysis of record statistics from the Gompertz model,” Applied Mathematics and Computation, vol. 145, no. 2-3, pp. 307–320, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. N. H. Gordon, “Maximum likelihood estimation for mixtures of two Gompertz distribution when censoring occurs,” Communications in Statistics-Simulation and Computation, vol. 19, pp. 733–747, 1990. View at Google Scholar
  14. Z. Chen, “Parameter estimation of the Gompertz population,” Biometrical Journal, vol. 39, no. 1, pp. 117–124, 1997. View at Google Scholar · View at Scopus
  15. J.-W. Wu, W.-L. Hung, and C.-H. Tsai, “Estimation of parameters of the Gompertz distribution using the least squares method,” Applied Mathematics and Computation, vol. 158, no. 1, pp. 133–147, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. M. L. Garg, B. R. Rao, and C. K. Redmond, “Maximum likelihood estimation of the parameters of the Gompertz survival function,” Journal of the Royal Statistical Society C, vol. 19, pp. 152–159, 1970. View at Google Scholar
  17. A. A. Ismail, “Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring,” Journal of Statistical Computation and Simulation, vol. 80, no. 11, pp. 1253–1264, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Al-Khedhairi and A. El-Gohary, “A new class of bivariate Gompertz distributions and its mixture,” International Journal of Mathematical Analysis, vol. 2, pp. 235–253, 2008. View at Google Scholar
  19. C.-C. Wu, S.-F. Wu, and H.-Y. Chan, “MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1657–1670, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. S.-J. Wu, C.-T. Chang, and T.-R. Tsai, “Point and interval estimations for the Gompertz distribution under progressive type-II censoring,” Metron, vol. 61, pp. 403–418, 2003. View at Google Scholar
  21. S. Kotz, Y. Lumelsdii, and M. Pensky, The Stress-Strength Model and Its Generalization, World Scientific, Singapore, 2003.
  22. B. Saraçoğlu and M. F. Kaya, “Maximum likelihood estimation and confidence intervals of system reliability for Gompertz distribution in stress-strength models,” Selçuk Journal of Applied Mathematics, vol. 8, no. 2, pp. 25–36, 2007. View at Google Scholar
  23. B. Saraçoǧlu, M. F. Kaya, and A. M. Abd-Elfattah, “Comparison of estimators for stress-strength reliability in the gompertz case,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 339–349, 2009. View at Google Scholar · View at Scopus
  24. A. C. Cohen, “Progressively censored samples in life testing,” Technometrics, vol. 5, pp. 327–329, 1963. View at Google Scholar
  25. D. R. Thomas and W. M. Wilson, “Linear order statistic estimation for the two parameter Weibull and extreme value distributions from Type II progressively censored samples,” Technometrics, vol. 14, pp. 679–691, 1972. View at Google Scholar
  26. P. N. Jani and H. P. Dave, “Minimum variance unbiased estimation in a class of exponential family of distributions and some of its applications,” Metron, vol. 48, no. 1–4, pp. 493–507, 1990. View at Google Scholar
  27. A. Shanubhogue and N. R. Jain, “Minimum variance unbiased estimation in exponential distribution using progressively type II censored data with binomial removals,” Advances and Applications in Statistics, vol. 18, pp. 27–39, 2010. View at Google Scholar
  28. M. M. King, D. M. Bailey, D. D. Gibson, J. V. Pitha, and P. B. McCay, “Incidence and growth of mammary tumors induced by 7,12-dimethylbenz[α]anthracene as related to the dietary content of fat and antioxidant,” Journal of the National Cancer Institute, vol. 63, no. 3, pp. 657–663, 1979. View at Google Scholar · View at Scopus
  29. E. T. Lee, Statistical Methods for Survival Data Analysis, Wiley, New York, NY, USA, 2nd edition, 1992.