World Academy of Science, Engineering and Technology
Published December 23, 2010 | Version 15474
Journal article Open

Estimation of R= P [Y < X] for Two-parameter Burr Type XII Distribution

Authors/Creators

Description

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Files

15474.pdf

Files (92.0 kB)

Name Size
md5:1b6ec2c799a292b1f66678ca5836e7d3
92.0 kB Preview Download

Additional details

References

  • I.W. Burr, "Cumulative frequency distribution," Annals of Mathematical Statistics vol. 13, 215-232, 1942.
  • H. Panahi, and S. Asadi, "Burr Type XII Distribution: Different Method of Estimations," The Tenth Islamic Countries Conference on Statistical Sciences The American University, Egypt, 2009.
  • I.G. Surles, and W.J. Padgett, "Inference for reliability and stressstrength for a scaled Burr Type X distribution," Lifetime Data Analysis vol. 7, [102] 187-200, 2001.
  • M.Z. Raqab, and D. Kundu, "Comparison of Different Estimators of P[Y < X] for a Scaled Burr Type X Distribution,- Communication in Statistics-Computations and Simulations vol. 34(2), 465-483, 2005.
  • Q. Shao, "Notes on maximum likelihood estimation for the threeparameter Burr XII distribution," Computational Statistics & Data Analysis vol. 45, 675 - 687, 2004.
  • D. Moore, and A.S. Papadopoulos, ÔÇÿThe Burr type XII distribution as a failure model under various loss functions,- Microelectronics Reliability 40, 2117-2122, 2000.
  • R.N. Rodriguez, "guide to Burr Type XII distributions," Biometrika vol. 64,129-134, 1977.
  • K.E. Ahmad, M.E. Fakhry, and Z.F. Jaheen, "Empirical Bayes estimation of P(Y < X) and characterization of Burr-type X model," Journal of Statistical Planning and Inference vol. 64, 297-308, 1997.
  • J.G. Surles, and W.J. Padgett, "Some properties of a scaled Burr type X distribution," Journal of Statistical Planning and Inference vol. 128, Issue 1, 271-280, 2005. [10] A.M. Abd-Elfattah, and R.M. Mandouh, ÔÇÿEstimation of Pr{Y<X} in Lomax case," The 39th Annual Conference on Statistics, Computer Science and Operation Research, ISSR, Cairo University, Egypt, part 1, 156-166, 2004. [11] D. Kundu, and R.D. Gupta, "Estimation of P(Y<X) for Generalized Exponential Distributions," Metrika 61(3), 291-308, 2005. [12] H. Tong, "A note on the estimation of P(Y<X) in the exponential case," Technometrics vol. 16, 625, 1974. (Errara, vol. 17, 395, 1975.) [13] H. Tong, "On the estimation of P(Y<X) for exponential families," IEE Transactions on Reliability vol. 26, 54-56, 1977.