Table of Contents
Journal of Probability
Volume 2014, Article ID 736101, 11 pages
http://dx.doi.org/10.1155/2014/736101
Research Article

The Generalized Inverse Generalized Weibull Distribution and Its Properties

Department of Statistics, Panjab University, Chandigarh 160014, India

Received 25 February 2014; Revised 2 July 2014; Accepted 8 July 2014; Published 6 August 2014

Academic Editor: Farrukh Mukhamedov

Copyright © 2014 Kanchan Jain et al. 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. G. S. Mudholkar and D. K. Srivastava, “Exponentiated Weibull family for analyzing bathtub failure-rate data,” IEEE Transactions on Reliability, vol. 42, no. 2, pp. 299–302, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. G. S. Mudholkar, D. K. Srivastava, and M. Friemer, “The exponentiated weibull family: a reanalysis of the bus-motor-failure data,” Technometrics, vol. 37, no. 4, pp. 436–445, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. G. S. Mudholkar and A. D. Hutson, “The exponentiated weibull family: some properties and a flood data application,” Communications in Statistics: Theory and Methods, vol. 25, no. 12, pp. 3059–3083, 1996. View at Publisher · View at Google Scholar · View at Scopus
  4. R. G. Voda, “On the inverse rayleigh variable,” Union of Japanese Scientists and Engineers, vol. 19, no. 4, pp. 15–21, 1972. View at Google Scholar
  5. P. Erto and M. Rapone, “Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model,” Reliability Engineering, vol. 7, no. 3, pp. 181–191, 1984. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Drapella, “ComplementaryWeibull distribution: unknown or just forgotten,” Quality and Reliability Engineering International, vol. 9, pp. 383–385, 1993. View at Google Scholar
  7. R. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Wiley-Interscience, New York, NY, USA, 2nd edition, 1995.
  8. P. Pawlas and D. Szynal, “Characterizations of the inverse Weibull distribution and generalized extreme value distributions by moments of k th record values,” Applicationes Mathematicae, vol. 27, no. 2, pp. 197–202, 2000. View at Google Scholar · View at MathSciNet
  9. A. Z. Keller, A. R. R. Kamath, and U. D. Perera, “Reliability analysis of CNC machine tools,” Reliability Engineering, vol. 3, no. 6, pp. 449–473, 1982. View at Publisher · View at Google Scholar · View at Scopus
  10. G. S. Mudholkar and G. D. Kolia, “Generalized Weibull family: a structural analysis,” Communications in Statistics Series A: Theory and Methods, vol. 23, pp. 1149–1171, 1994. View at Google Scholar
  11. D. N. P. Murthy, M. Xie, and R. Jiang, Weibull Models, John Wiley & Sons, New York, NY, USA, 2004.
  12. R. Calabria and G. Pulcini, “Bayes 2-sample prediction for the inverse weibull distribution,” Communications in Statistics—Theory and Methods, vol. 23, no. 6, pp. 1811–1824, 1994. View at Publisher · View at Google Scholar
  13. M. Aleem and G. R. Pasha, “Ratio, product and single moments of order statistics from inverse Weibull distribution,” Journal of Statistics, vol. 10, no. 1, pp. 1–7, 2003. View at Google Scholar
  14. F. R. S. de Gusmão, E. M. M. Ortega, and G. M. Cordeiro, “The generalized inverse Weibull distribution,” Statistical Papers, vol. 52, no. 3, pp. 591–619, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. B. S. Everitt and D. J. Hand, Finite Mixture Distributions, Chapman & Hall, London, UK, 1981.
  16. G. J. Maclachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley & Sons, New York, NY, USA, 1997.
  17. G. Maclachlan and D. Peel, Finite Mixture Models, John Wiley & Sons, New York, NY, USA, 2000.
  18. E. K. AL-Hussaini and K. S. Sultan, “Reliability and hazard based on nite mixture models,” in Handbook of Statistics, N. Balakrishnan and C. R. Rao, Eds., vol. 20, pp. 139–183, Elsevier, Amsterdam, The Netherlands, 2001. View at Google Scholar
  19. R. Jiang, D. N. P. Murthy, and P. Ji, “Models involving two inverse Weibull distributions,” Reliability Engineering and System Safety, vol. 73, no. 1, pp. 73–81, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. K. S. Sultan, M. A. Ismail, and A. S. Al-Moisheer, “Mixture of two inverse Weibull distributions: properties and estimation,” Computational Statistics and Data Analysis, vol. 51, no. 11, pp. 5377–5387, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. H. Teicher, “Identifiability of finite mixtures,” Annals of Mathematical Statistics, vol. 34, pp. 1265–1269, 1963. View at Publisher · View at Google Scholar · View at MathSciNet
  22. S. Chandra, “On the mixtures of probability distributions,” Scandinavian Journal of Statistics, vol. 4, no. 3, pp. 105–112, 1977. View at Google Scholar · View at MathSciNet
  23. J. P. Klein and M. L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, Springer, New York, NY, USA, 2003.
  24. B. J. Sickle-Santanello, W. B. Farrar, S. Keyhani-Rofagha et al., “A reproducible System of flow cytometric DNA analysis of paraffin embedded solid tumors: technical improvements and statistical analysis,” Cytometry, vol. 9, pp. 594–599, 1988. View at Publisher · View at Google Scholar