Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 263612, 11 pages
Research Article

Inference on P r ( 𝑋 < 𝑌 ) in the Two-Parameter Weibull Model Based on Records

Department of Mathematics and Physics, College of Arts and Sciences, Qatar University, Doha 2713, Qatar

Received 2 April 2012; Accepted 21 June 2012

Academic Editors: S. Lototsky, V. Makis, M. Montero, and P. Neal

Copyright © 2012 Ayman Baklizi. 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. K. N. Chandler, “The distribution and frequency of record values,” Journal of the Royal Statistical Society B, vol. 14, pp. 220–228, 1952. View at Google Scholar · View at Zentralblatt MATH
  2. M. Ahsanullah, Record Values: Theory and Applications, University Press of America, Lanham, Md, USA, 2004. View at Zentralblatt MATH
  3. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records, Wiley, 1998. View at Zentralblatt MATH
  4. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vol. 1, John Wiley & Sons, New York, NY, USA, 1994.
  5. D. N. P. Murthy, M. Xie, and R. Jiang, Weibull Models, Wiley Series in Probability and Statistics, Wiley, 2004.
  6. I. J. Hall, “Approximate one-sided tolerance limit for the difference or sum of two independent random variates,” Journal of Quality Technology, vol. 16, no. 1, pp. 15–19, 1984. View at Google Scholar · View at Scopus
  7. S. Weerahandi and R. A. Johnson, “Testing reliability in a stress-strength model when X and Y are normally distributed,” Technometrics, vol. 34, no. 1, pp. 83–91, 1992. View at Google Scholar · View at Scopus
  8. S. Kotz, Y. Lumelskii, and M. Pensky, The Stress-Strength Model and Its Generalizations: Theory and Applications, World Scientific, 2003.
  9. A. Baklizi, “Estimation of Pr (X < Y) using record values in the one and two parameter exponential distributions,” Communications in Statistics. Theory and Methods, vol. 37, no. 5, pp. 692–698, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Baklizi, “Likelihood and Bayesian estimation of Pr (X < Y) using lower record values from the generalized exponential distribution,” Computational Statistics and Data Analysis, vol. 52, no. 7, pp. 3468–3473, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Kundu and R. D. Gupta, “Estimation of P [Y < X] for Weibull distributions,” IEEE Transactions on Reliability, vol. 55, no. 2, pp. 270–280, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. M. H. Chen and Q. M. Shao, “Monte carlo estimation of bayesian credible and HPD interval,” Journal of Computational and Graphical Statistics, vol. 8, no. 1, pp. 69–92, 1999. View at Google Scholar · View at Scopus
  13. B. Efron and R. J. Tibshirani, An Introduction To the Bootstrap, Chapman & Hall, 1993.