Estimate the Shape Parameter for the Kumaraswamy Distribution via Some Estimation Methods


Abstract views: 118 / PDF downloads: 98

Authors

Keywords:

Kumaraswamy, Shape Parameter, Rank set, LINEX, Double priors

Abstract

This paper shows how to estimate one of the two shape parameters of Kumaraswamy distribution using two estimation methods. The first one is the rank set sampling estimation method and the second one is the Bayes estimation method. The rank set sampling was employed as a non-Bayes estimator. In addition, Bayes estimators were used based on asymmetric loss function (LINEX) by utilizing four kinds of informative prior (one single prior and three double prior). Comparisons were made between different estimators using a Monte Carlo simulation study and the shape parameter estimates were compared depending on the mean squared error. Finally, the program (MATLAB 2015) was used to get the mathematical outcomes.

References

P. Kumaraswamy, “A generalized probability density function for double-bounded random processese,” J. Hydrol., vol. 46, no. 1–2, pp. 79–88, 1980.

N. H. Al-Noor and Sudad K. Ibraheem, “ON THE MAXIMUM LIKELIHOOD, BAYES AND EMPIRICAL BAYESESTIMATION FOR THE SHAPE PARAMETER, RELIABILITY ANDFAILURE RATE FUNCTIONS OF KUMARASWAMYDISTRIBUTION,” Glob. J. Bio-Science Biotechnol., vol. 5, no. 1, pp. 128–134, 2016.

F. Sultana, Y. M. Tripathi, M. K. Rastogi, and S. J. Wu, “Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring,” Am. J. Math. Manag. Sci., vol. 37, no. 3, pp. 243–261, 2018, doi: 10.1080/01966324.2017.1396943.

R. A. R. Bantan, F. Jamal, C. Chesneau, and M. Elgarhy, “Truncated inverted Kumaraswamy generated family of distributions with applications,” Entropy, vol. 21, no. 11, 2019, doi: 10.3390/e21111089.

I. Ghosh, “Bivariate and Multivariate Weighted Kumaraswamy Distributions: Theory and Applications,” J. Stat. Theory Appl., vol. 18, no. 3, p. 198, 2019, doi: 10.2991/jsta.d.190619.001.

S. K. Abraheem, N. J. Fezaa Al-Obedy, and A. A. Mohammed, “A comparative study on the double prior for reliability kumaraswamy distribution with numerical solution,” Baghdad Sci. J., vol. 17, no. 1, pp. 159–165, 2020, doi: 10.21123/bsj.2020.17.1.0159.

M. A. Mahmoud, A. A. Mohammed, and ..., “A comparative study on numerical, non-Bayes and Bayes estimation for the shape parameter of Kumaraswamy distribution,” Int. J. …, vol. 13, no. 1, pp. 1417–1434, 2022.

R. Gholizadeh, A. M. Shirazi, and S. Mosalmanzadeh, “Classical and Bayesian Estimations on the Kumaraswamy Distribution using Grouped and Un-grouped Data under Difference Loss Functions,” J. Appl. Sci., vol. 11, no. 12, pp. 2154–2162, 2011.

G. P. Patil, A. K. Sinha, and C. Taillie, “5 Ranked set sampling,” Handb. Stat., vol. 12, pp. 167–200, 1994.

S. S. Alwan, “Non-Bayes, Bayes and Empirical Bayes Estimator for Lomax Distribution,” A thesis Submitt. to Counc. Coll. scince Al-Mustansiriya Univ. Partial Fulfillment Requir. degree Master Sci. Math., 2015.

A. F. M. Saiful Islam, “Loss functions , utility functions and Bayesian sample size determination,” A Thisis is Submitted for the Degree of Doctor of Philosophy in Queen Mary, University of London, 2011.

R. Sultan, H. Sultan, and S. P. Ahmad, “Bayesian Analysis of Power Function Distribution under Double Priors,” J. Stat. Appl. Probab., vol. 3, no. 2, pp. 239–249, 2014, doi: 10.12785/jsap/030214.

R. M. Patel and A. S. Patel, “THE DOUBLE PRIOR SELECTION FOR THE PARAMETER OF POWER FUNCTION DISTRIBUTION UNDER TYPE-II CENSORING,” Int. J. Curr. Res., vol. 8, no. 05, pp. 30454–30465, 2016.

R. M. Patel and A. C. Patel, “The double prior selection for the parameter of exponential life time model under type II censoring,” J. Mod. Appl. Stat. Methods, vol. 16, no. 1, pp. 406–427, 2017, doi: 10.22237/jmasm/1493598180.

Downloads

Published

2024-02-08

How to Cite

K. Abraheem, S., Yasmin Hamed Abd, & A. Mohammed, A. (2024). Estimate the Shape Parameter for the Kumaraswamy Distribution via Some Estimation Methods. Results in Nonlinear Analysis, 7(1), 142–155. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/303