Some methods to approximate and estimate the reliability function of inverse Rayleigh distribution
Abstract views: 143
/ 
PDF downloads: 162
Keywords:
Inverse Rayleigh, Maximum-likelihood, NLINEX loos function, Chi-squared, Bernstein polynomialsAbstract
In this paper, three methods to find the reliability function for inverse Rayleigh distribution are introduced. The first one, the reliability function is expanded using Bernstein polynomials to find the approximate solution of it. The second one, the maximum likelihood is applied to estimate the scale parameter to find the reliability function. The third one, the Bayes estimator is developed under the NLINEX loss function to find the reliability function with the least loss where this estimator is derived using chi-squared informative prior distribution. The results of all methods depending on the integrated mean squared error (IMSE) are compared to find which of these methods is best by using the simulation technique. Finally, to determine theoretical results MATLAB 2015 is used.
References
M. Mohsin and M. Q. Shahbaz, “Comparison of Negative Moment Estimator with Maximum Likelihood Estimator of Inverse Rayleigh Distribution,” Pakistan J. Stat. Oper. Res., vol. 1, no. 1, pp. 45–48, 2005, doi: 10.18187/pjsor.v1i1.115.
S. Dey, “Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution,” Malaysian J. Math. Sci., vol. 6, no. 1, pp. 113–124, 2012.
G. Fan, “Bayes estimation for inverse rayleigh model under different loss functions,” Res. J. Appl. Sci. Eng. Technol., vol. 9, no. 12, pp. 1115–1118, 2015, doi: 10.19026/rjaset.9.2605.
K. Fatima and S. P. Ahmad, “Weighted Inverse Rayleigh Distribution,” Int. J. Stat. Syst., vol. 12, no. 1, pp. 119–137, 2017.
F. Ardianti and Sutarman, “Estimating parameter of Rayleigh distribution by using Maximum Likelihood method and Bayes method,” IOP Conf. Ser. Mater. Sci. Eng., vol. 300, pp. 012036(1–5), 2018, doi: 10.1088/1757-899X/300/1/012036.
A. A. Mohammed, S. K. Abraheem, and N. J. F. Al-Obedy, “Bayesian Estimation of Reliability Burr Type XII under Al-Bayyatis’ Suggest Loss Function with Numerical Solution,” J. Phys. Conf. Ser., vol. 1003, no. 1, pp. 1–16, 2018, doi: 10.1088/1742-6596/1003/1/012041.
B. A. A. Ali, H. M. Gorgees, and R. I. Kathim, “Bayesian estimators of the scale parameter and reliability function of inverse Rayleigh distribution under three types of loss function,” AIP Conf. Proc., vol. 2290, pp. 040018–1–040018–5, 2020, doi: 10.1063/5.0027983.
A. Yunus, Ö. Egemen, K. Kadir, and T. Caner, “Estimation of Parameter for Inverse Rayligh Distribution under Type-I Hybrid Censored Samples,” Sigma J. Eng. Nat. Sci., vol. 38, no. 4, pp. 1705–1711, 2020.
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.
R. R. Abu Awwad, O. M. Bdair, and G. K. Abufoudeh, “Bayesian estimation and prediction based on Rayleigh record data with applications,” Stat. Transit. New Ser., vol. 23, no. 3, pp. 59–79, 2021, doi: 10.21307/STATTRANS-2021-027.
M. A. Mahmoud, S. K. Abraheem, and A. A. Mohammed, “On the maximum likelihood , Bayes and expansion estimation for the reliability function of Kumaraswamy distribution under different loos function,” Int. J. Nonlinear Anal. Appl., vol. 13, no. October 2021, pp. 1587–1604, 2022.
A. R. Huda and K. A. Raghda, “Bayesian Approach in Estimation of Scale Parameter of Inverse Rayleigh Distribution,” Math. Stat. J., vol. 2, no. 1, pp. 8–13, 2016.
J. T. Abdullah, “Numerical solution for linear fredholm integro-differential equation using touchard polynomials,” Baghdad Sci. J., vol. 18, no. 2, pp. 330–337, 2021, doi: 10.21123/BSJ.2021.18.2.0330.
S. Bazm, “Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations,” J. Comput. Appl. Math., vol. 275, pp. 44–60, 2015, doi: 10.1016/j.cam.2014.07.018.
Y. Şimşek, “Generating functions for the bernstein type polynomials: A new approach to deriving identities and applications for the polynomials,” Hacettepe J. Math. Stat., vol. 43, no. 1, pp. 1–14, 2014.
I. Kucukoglu and Y. Simsek, “New Formulas and Numbers Arising from Analyzing Combinatorial Numbers and Polynomials,” Montes Taurus J. Pure Appl. Math., vol. 3, no. 3, pp. 238–259, 2021.
R. N. Shalan and I. H. Alkanani, “Some Methods to Estimate the Parameters of Generalized Exponential Rayleigh Model by Simulation,” Iraqi J. Comput. Sci. Math., vol. 4, no. 2, pp. 118–129, 2023.
A. S. Hassan, S. M. Assar, and A. M. A. Elghaffar, “Bayesian estimation of power transmuted inverse rayleigh distribution,” Thail. Stat., vol. 19, no. 2, pp. 393–410, 2021.
A. F. M. Islam, M. K. Roy, and M. M. Ali, “A Non-Linear Exponential(NLINEX) Loss Function in Bayesian Analysis,” J. Korean Data Inf. Sci. Soc., vol. 15, no. 4, pp. 899–910, 2004.
J. Mahanta and H. Rahman, “A Non-Linear Loss Function ( NL ) in Bayesian Approach,” Chittagong Univ. J. Sci., vol. 39, no. September, pp. 119–134, 2017.
A. A. Soliman, “Comparison of linex and quadratic bayes estimators for the rayleigh distribution,” Commun. Stat. - Theory Methods, vol. 29, no. 1, pp. 95–107, 2000, doi: 10.1080/03610920008832471.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
