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The Scientific World Journal
Volume 2014, Article ID 512039, 6 pages
http://dx.doi.org/10.1155/2014/512039
Research Article

Estimation of the Parameters of Burr Type III Distribution Based on Dual Generalized Order Statistics

1Department of Applied Mathematics, Kongju National University, Gongju 314-701, Republic of Korea
2Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242-1409, USA

Received 12 June 2014; Accepted 16 September 2014; Published 19 October 2014

Academic Editor: Krzysztof Malarz

Copyright © 2014 Chansoo Kim and Woosuk Kim. 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. I. W. Burr, “Cumulative frequency functions,” Annals of Mathematical Statistics, vol. 13, pp. 215–232, 1942. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. H. Gove, M. J. Ducey, W. B. Leak, and L. Zhang, “Rotated sigmoid structures in managed uneven-aged northern hardwood stands: a look at the Burr Type III distribution,” Forestry, vol. 81, no. 2, pp. 161–176, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. P. W. Mielke, “Another family of distributions for describing and analyzing precipitation data,” Journal of Applied Meteorology, vol. 12, pp. 275–280, 1973. View at Publisher · View at Google Scholar
  4. N. A. Mokhlis, “Reliability of a stress-strength model with Burr type III distributions,” Communications in Statistics. Theory and Methods, vol. 34, no. 7, pp. 1643–1657, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. I. W. Burr and P. J. Cislak, “On a general system of distributions, I: its curve-shape characteristics, II: the sample median,” Journal of the American Statistical Association, vol. 63, pp. 627–635, 1968. View at Publisher · View at Google Scholar · View at MathSciNet
  6. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, John Wiley & Sons, New York, NY, USA, 2nd edition, 1995.
  7. A. M. Abd-Elfattah and A. H. Alharbey, “Bayesian estimation for Burr distribution type III based on trimmed samples,” ISRN Applied Mathematics, vol. 2012, Article ID 250393, 18 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. U. Kamps, “A concept of generalized order statistics,” Journal of Statistical Planning and Inference, vol. 48, no. 1, pp. 1–23, 1995. View at Google Scholar
  9. M. Burkschat, E. Cramer, and U. Kamps, “Dual generalized order statistics,” Metron. International Journal of Statistics, vol. 61, no. 1, pp. 13–26, 2003. View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Ahsanullah, “A characterization of the uniform distribution by dual generalized order statistics,” Communications in Statistics. Theory and Methods, vol. 33, no. 11-12, pp. 2921–2928, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Z. F. Jaheen, “Estimation based on generalized order statistics from the Burr model,” Communications in Statistics: Theory and Methods, vol. 34, no. 4, pp. 785–794, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. K. Mbah and M. Ahsanullah, “Some characterizations of the power function distribution based on lower generalized order statistics,” Pakistan Journal of Statistics, vol. 23, no. 2, pp. 139–146, 2007. View at Google Scholar · View at MathSciNet
  13. H. M. Barakat and M. E. El-Adll, “Asymptotic theory of extreme dual generalized order statistics,” Statistics & Probability Letters, vol. 79, no. 9, pp. 1252–1259, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. W. Kim and C. Kim, “On dual generalized order statistics from Burr Type III distribution and its characterization,” Far East Journal of Mathematical Sciences, vol. 81, no. 1, pp. 21–39, 2013. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. D. V. Lindley, “Approximat e bayesian methods,” Trabajos de Estadistica, vol. 21, pp. 223–237, 1980. View at Google Scholar