Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2015 (2015), Article ID 159710, 6 pages
http://dx.doi.org/10.1155/2015/159710
Research Article

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

1Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt
2Department of Mathematics and Statistics, Faculty of Science, Taif University, Hawia 888, Saudi Arabia
3Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, Egypt

Received 25 June 2015; Accepted 7 September 2015

Academic Editor: Chunsheng Ma

Copyright © 2015 M. M. Mohie EL-Din 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. N. L. Johnson and S. Kotz, “On some generalized Farlie-Gumbel-Morgenstern distributions,” Communications in Statistics, vol. 4, no. 5, pp. 415–427, 1975. View at Google Scholar · View at MathSciNet
  2. H. A. David, M. J. O'Connell, and S. S. Yang, “Distribution and expected value of the rank of a concomitant of an order statistic,” The Annals of Statistics, vol. 5, no. 1, pp. 216–223, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  3. U. Kamps, “A concept of generalized order statistics,” Journal of Statistical Planning and Inference, vol. 48, no. 1, pp. 1–23, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. U. Kamps and E. Cramer, “On distributions of generalized order statistics,” Statistics, vol. 35, no. 3, pp. 269–280, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  5. P. Pawlas and D. Szynal, “Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution,” Demonstratio Mathematica, vol. 34, no. 2, pp. 353–358, 2001. View at Google Scholar · View at MathSciNet
  6. M. Burkschat, E. Cramer, and U. Kamps, “Dual generalized order statistics,” Metron, vol. 61, no. 1, pp. 13–26, 2003. View at Google Scholar · View at MathSciNet
  7. M. I. Beg and M. Ahsanullah, “Concomitants of generalized order statistics from Farlie-Gumbel-Morgenstern distributions,” Statistical Methodology, vol. 5, no. 1, pp. 1–20, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Nayabuddin, “Concomitants of dual generalized order statistics from Farlie Gumbel Morgenstern type bivariate power function distribution,” Journal of Global Research in Mathematical Archives, vol. 1, no. 8, pp. 79–90, 2013. View at Google Scholar
  9. M. M. Mohie El-Din, M. M. Ameina, and M. S. Mohamed, “Concomitants of case-II of generalized order statistics from Farlie-Gumbel-Morgenstern distributions,” Journal of Statistics Applications and Probability, vol. 3, no. 3, pp. 345–353, 2015. View at Google Scholar
  10. C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948. View at Publisher · View at Google Scholar · View at MathSciNet
  11. N. Ebrahimi, “How to measure uncertainty in the residual life time distribution,” Sankhyā. The Indian Journal of Statistics A, vol. 58, no. 1, pp. 48–56, 1996. View at Google Scholar · View at MathSciNet
  12. A. Di Crescenzo and M. Longobardi, “Entropy-based measure of uncertainty in past lifetime distributions,” Journal of Applied Probability, vol. 39, no. 2, pp. 434–440, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. R. C. Gupta, H. C. Taneja, and R. Thapliyal, “Stochastic comparisons of residual entropy of order statistics and some characterization results,” Journal of Statistical Theory and Applications, vol. 13, no. 1, pp. 27–37, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. R. C. Gupta and S. N. U. A. Kirmani, “Characterization based on convex conditional mean function,” Journal of Statistical Planning and Inference, vol. 138, no. 4, pp. 964–970, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. W. J. Hall and J. A. Wellner, “Mean residual life,” in Statistics and Related Topics, pp. 169–184, North-Holland, Amsterdam, The Netherlands, 1981. View at Google Scholar · View at MathSciNet
  16. D. Oakes and T. Dasu, “A note on residual life,” Biometrika, vol. 77, no. 2, pp. 409–410, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus