International Journal of Nonlinear Analysis and Applications

Comparison of some Bayesian shrinkage estimation for Frechet distribution with simulations

Document Type : Research Paper

Authors

1 Department of Statistics, Faculty of Administration and Economics, Kerbala University, Iraq

2 AL Amall Collage, Kerbala, Iraq

Abstract

The Frechet distribution is one of the important statistical distributions and it has many applications, especially in the field of distributing the maximum extent of disease precipitation and river drainage, and estimating the parameters of the Frechet distribution is very important, and for that research came in an attempt to compare several methods of estimating the parameter of Frechet distribution based on different Bayesian methods with (square loss, Linux and Unix) functions. In this research, several simulation experiments were conducted according to the difference in (sample size, value of distribution parameters and estimation methods) and the results were compared based on mean square error criteria, it is possible to use other estimation methods such as (moments and percentile), for other distributions such as (Gumbel and Lindley).

Keywords

[1] A.Z. Afify, G. Hamedani, I. Ghosh and M. Mead, The transmuted Marshall-Olkin Fr´echet distribution: Properties and applications, Math. Stat. Comput. Sci. Faculty Res. Pub. 4 (2014), no. 4.
[2] A.Z. Afify, H.M. Yousof, G.M. Cordeiro, E.M.M. Ortega and Z.M. Nofal, The Weibull Fr´echet distribution and its applications, J. Appl. Stat. 43 (2016), no. 14, 2608–2626.
[3] E.M. Almetwally and H.Z. Muhammed, On a bivariate Fr´echet distribution, J. Stat. Appl. Probab. 9 (2020), no. 1, 1–21.
[4] A. Drapella, The complementary Weibull distribution: unknown or just forgotten?, Qual. Reliab. Eng. Int. 9 (1993), no. 4, 383–385.
[5] R.A. Fisher, A mathematical examination of the methods of determining the accuracy of an observation by the mean error, and by the mean square error, Month. Notices Royal Astronom. Soc. 80 (1920), 758–770.
[6] G.S. Mudholkar, D.K. Srivastava and G.D. Kollia, A generalization of the Weibull distribution with application to the analysis of survival data, J. Amer. Statist. Assoc. 91 (1996), no. 436, 1575–1583.
[7] S. Nadarajah and S. Kotz, The exponentiated Fr´echet distribution, Int. stat. Electr. J. 14 (2003), 1–7.
[8] P.L. Ramos, F. Louzada, E. Ramos and S. Dey, The Fr´echet distribution: Estimation and application-An overview, J. Stat. Manag. Syst. 23 (2020), no. 3, 549–578.
[9] W. Rodeen and S. Aziz, Bayes pre-test shrinkage estimators of scale parameter for Maxwell distribution under squared loss functions, J. Phys.: Conf. Ser. 1963 (2021), no. 1, 012069.
[10] H.M. Yousof, A.Z. Afify, N.E. Abd El Hadi, G.G. Hamedani and N.S. Butt, On six-parameter Fr´echet distribution: Properties and applications, Pakistan J. Stat. Oper. Res. 12 (2016), no. 2, 281–299.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 2265-2278
  • Receive Date: 05 August 2022
  • Revise Date: 26 September 2022
  • Accept Date: 11 November 2022