Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 297–303 | Cite as

Bayesian Estimation Using (Linex) for Generalized Power Function Distribution

  • Alya O. Al Mutairi


This paper introduced the Bayesian estimation when the loss function is a linear exponential (LINEX) for shape parameters from a generalized power function distribution. A numerical application is used to prove the accuracy of this method by comparing it with other non-Bayesian methods of estimation as the maximum likelihood.


Generalized power function distribution LINEX power function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Meniconi and D. M. Barry, “The power function distribution: a useful and simple distribution to assess electrical component reliability,” Microelectron. Reliab. 36, 1207–1212 (1996).CrossRefGoogle Scholar
  2. 2.
    P. R. Rider, “Distribution of product and of quotient of maximum values in samples from a power-function population,” J. Am. Stat. Assoc. 59, 877–880 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    H. J. Malik, “Exact moments of order statistics from a power-function distribution,” Scand. Actuar. J. 1–2, 64–69 (1967).MathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Lwin, “Estimation of the tail of the Paretian law,” Scand. Actuar. J. 2, 170–178 (1972).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    B. C. Arnold and S. J. Press, “Bayesian inference for Pareto populations,” J. Econom. 21, 287–306 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    A. B. M. Lutful Kabir and M. Ahsanullah, “Estimation of the location and scale parameters of a powerfunction distribution by linear functions of order statistics,” Commun. Stat. Theory Methods 3, 463–467 (1974).CrossRefzbMATHGoogle Scholar
  7. 7.
    A. S. Samia and M. M. Mohammed, “Modified Moment Estimators for three parameters Pareto distribution,” Inst. Stat. Study Res., Cairo Univ. 28, 2 (1993).Google Scholar
  8. 8.
    S. Lalitha and A. Mishra, “Modified maximum likelihood estimation for Rayleigh distribution,” Commun. Stat. TheoryMethods 25, 389–401 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Rafiq, “Estimation of parameters of the Gamma distribution by the method of fractional moments,” Pakistan J. Stat. 12, 265–274 (1996).Google Scholar
  10. 10.
    N. B. Marks, “Estimation ofWeibull parameters from common percentiles,” J. Appl. Stat. 32, 17–24 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    A. Zaka and A. S. Akhter, “Methods for estimating the parameters of the power function distribution,” Pakistan J. Stat. Oper. Res. 9, 213–224 (2013).MathSciNetCrossRefGoogle Scholar
  12. 12.
    G. S. Saluja, M. Postolache, and A. Kurdi, “Convergence of three-step iterations for nearly asymptotically non expansive mappings in CAT (k) spaces,” J. Inequal. Appl. 1, 1–18 (2015).zbMATHGoogle Scholar
  13. 13.
    R. Maiti and A. Biswas, “Coherent forecasting for over-dispersed time series of count data,” Braz. J. Probab. Stat. 29, 747–766 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    H. R. Varian, “A Bayesian approach to real estate assessment,” in Studies in Bayesian Econometrics and Statistics in Honor of J. Leonard, Savage, Ed. by S. E. Fienberg and A. Zellner (North-Holland, Amsterdam, 1974), pp. 195–208.Google Scholar
  15. 15.
    A. Zellner, “Bayesian estimation and prediction under asymmetric loss functions,” J. Am. Stat. Assoc. 81, 446–451 (1986).CrossRefzbMATHGoogle Scholar
  16. 16.
    P. F. Christoffersen and F. X. Diebold, “Optimal prediction under asymmetric loss,” Econom. Theor. 13, 808–817 (1997).MathSciNetCrossRefGoogle Scholar
  17. 17.
    R. Batchelor and D. A. Peel, “Rationality testing under asymmetric loss,” Econ. Lett. 61, 49–54 (1998).CrossRefzbMATHGoogle Scholar
  18. 18.
    A. J. Patton and A. Timmermann, “Properties of optimal forecasts under asymmetric loss and nonlinearity,” J. Econom. 140, 884–918 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    S. Anatolyev, “Kernel estimation under linear-exponential loss,” Econ. Lett. 91, 39–43 (2006).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTaibah UniversityMedinaSaudi Arabia

Personalised recommendations