Comparison of Estimation Methods for the Parameters of the Frechet Distribution - using Simulation.
Abstract
Probability distributions are mathematical functions that describe the likelihood of different outcomes in random process estimates for the scale parameters and the shape parameter according to the type of data that can determine the appropriate probability distribution. In this paper, an experimental study is presented to compare a number of estimation methods for the parameters of the Frechet distribution, which is one of the most important probability distributions in the fields of determining failure times. The estimation Methods are (Maximum Likelihood, Moments and Bayesian methods) were adopted. Through the simulation method, the comparison process was carried out, where the experimental samples were determined (n = 15, 25, 50, 75, 100) with the assumption of four default values for each of the shape parameter ( =1.1, 1.5, 2, 2.5) and the scale parameter (=1.4, 1.8, 2.3, 3). Through this method, the paper was able to determine the appropriate method for estimation by adopting the Mean square error criterion. The experimental results showed the superiority of the Bayes method. Then the method of Maximum likelihood.
References
- Al Wakeel, K. H., & Laibi, A. I. (2019). Comparison of the weighted probability moments method with the general robust weighted probability moments method for estimating the parameters of the two-parameter power function distribution with a practical application. Journal of Administration and Economics, 2(122), 519-528. Retrieved from https://admics.uomustansiriyah.edu.iq/index.php/admeco/article/view/277
- Al-Yasiri, T. M. (2007). A Comparison of Robust Bayesian Estimators With Another Estimators To Estimate The Approximation of Reliability Function For Weibull Distribution. Ph.D of statistics, University of Baghdad, Administration and Economics of Gollege.
- Alharbi, T., & Hamad, F. (2024). An Optimal Strategy for Estimating Weibull distribution Parameters by Using Maximum Likelihood Method. Statistics, Optimization & Information Computing, 12(5), 1342-1351. doi:https://doi.org/10.19139/soic-2310-5070-2019
- Catelani, M., Ciani, L., Guidi, G., & Venzi, M. (2016). Parameter estimation methods for failure rate distributions. 14th IMEKO TC10 Workshop New Perspectives in Measurements, Tools and Techniques for systems reliability, maintainability and safety. Milan, Italy: IMEKO TC10. Retrieved from https://www.imeko.info/publications/tc10-2016/IMEKO-TC10-2016-083.pdf
- Ciani, L., & Guidi, G. (2019). Application and analysis of methods for the evaluation of failure rate distribution parameters for avionics components. Measurement, 139, 258-269. doi:https://doi.org/10.1016/j.measurement.2019.02.082
- Gove, J. H. (2003). Moment and maximum likelihood estimators for Weibull distributions under length- and area-biased sampling. Environmental and Ecological Statistics, 10(4), 455467. doi:https://doi.org/10.1023/A:1026000505636
- Grzenda, W. (2016). Informative versus non-informative prior distributions and their impact on the accuracy of Bayesian inference. Statistics in Transition New Series, 17(4), 763-780. doi:https://doi.org/10.21307/stattrans-2016-051
- Hansen, L. P. (1982). Large Sample Properties of Generalized Method of Moments Estimators. The Econometric Society; JSTOR, 50(4), 1029-1054. doi:https://doi.org/10.2307/1912775
- Harter, H., & Moore, A. (1965). Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples. 7(4), 639-643. doi:https://doi.org/10.2307/1266401
- Khader, A. J., Hassoun, A. O., & Hussein, A. N. (2009). The smallest order statistics from an exponential distribution also, has an exponential distribution. journal of Economics And Administrative Sciences, 15(53), 200-222. Retrieved from https://www.iasj.net/iasj/article/3078
- Khdair, M. S., & Aboudi, E. H. (2022). Comparison of Some Methods for Estimating the Survival Function and Failure Rate for the Exponentiated Expanded Power Function Distribution. Journal of Economics and Administrative Sciences, 23(133), 114-130. doi:https://doi.org/10.33095/jeas.v28i133.2354
- Muehlemann, N., Zhou, T., Mukherjee, R., Hossain, I. M., & Roychoudhury, S. (2023). A Tutorial on Modern Bayesian Methods in Clinical Trials. Therapeutic Innovation & Regulatory Science, 57, 402416. doi:https://doi.org/10.1007/s43441-023-00515-3
- Noaman, I. A., Abdul Ameer, H. A., & Mohammed, W. S. (2023). Comparison of Weibull and Frchet distributions estimators to determine the best areas of rainfall in Iraq. Periodicals of Engineering and Natural Sciences, 11(2), 275-283. Retrieved from file:///C:/Users/alMasarcc/Downloads/Documents/3527-8110-1-PB.pdf
- Ramos, P. L., Louzada, F., Ramos, E., & Dey, S. (2020). The Frchet distribution : Estimation and application - An overview. Journal of Statistics and Management Systems, 23(3), 549-578. doi:https://doi.org/10.1080/09720510.2019.1645400
- Tablada, C. J., & Cordeiro, G. M. (2017). The modified Frchet distribution and its properties. Communications in Statistics - Theory and Methods, 46(21), 10617-10639. doi:https://doi.org/10.1080/03610926.2016.1239115
