Lazim KAMBERİ, Senad ORHANİ, Mirlinda SHAQİRİ, Sejhan IDRİZİ

Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method

Important distributions used to model and analyse data in various real-life sciences such as natural sciences, engineering, and medicine are the Weibull, Weibull exponential, and Weibull Rayleigh distribution. The main objective of this paper is to determine the best evaluators and compare them for the distribution with three-parameters of Weibull, Weibull Rayleigh and Exponential Weibull. The methods under consideration for comparing the parameter estimators for these distributions is that of maximum likelihood using the statistical program R for the application of real data. Based on the results obtained from this study, the maximum likelihood approach used in estimating the parameters is the comparison between these distributions.

Keywords:

Exponential Weibull distribution maximum likelihood, parameters, Weibull distribution, Weibull-Rayleigh distribution,

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[1] G. T. Basheer, Z. Y. Algamal, “Reliability Estimation of Three Parameters Weibull Distribution based on Particle Swarm Optimization”, Pakistan Journal of Statistics and Operation Research, vol. 17, pp. 35-42, 2021.
[2] A. M. Abd Elfattah, A. S. Hassanand, D.M. Ziedan, “Efficiency of Maximum Likelihood Estimators under Different Censored Sampling Schemes for Rayleigh Distribution”, Interstat, 2006.
[3] R. D. Gupta, D. Kundu, “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrika Journal, vol. 43, pp. 117-130, 2001.
[4] E. K. AL-Hussaini, M. Ahsanullah, “Exponentiated Distributions”, Springer, vol. 5, 2015.
[5] G. S. Mudholkar, A. D. Hustson, “The exponentiated Weibull family: some properties and a flood data application”, Communications in Statistics-Theory and Methods, vol 25, pp. 3059-3083, 1996.
[6] K. Cooray, “Generalization of the Weibull distribution: the odd Weibull family”, Statistical Modelling, vol. 6, pp. 265-277, 2006.
[7] B. Marcelo, R. B. Silva , G. Cordeiro, “The Weibull - G Family of Probability Distributions”. Journal of Data Science, vol. 12, pp. 53-68, 2014.
[8] W. Barreto-Souza, A.H.S. Santos, G.M. Cordeiro, “The beta generalized exponential distribution”, Journal of Statistical Computation and Simulation, vol. 80, pp. 159-172, 2010.
[9] W. Barreto-Souza, A. L. Morais, G.M. Cordeiro, “The Weibull-geometric distribution”, Journal of Statistical Computation and Simulation, vol. 81, pp. 645-657, 2011.
[10] A. L. Morais, W. Barreto-Souza, “A compound class of Weibull and power series distributions”, Computational Statistics and Data Analysis, vol. 55, pp. 1410-1425, 2011.
[11] A. Choudhury, “A Simple derivation of moments of the exponentiated Weibull distribution”, Metrika, vol. 62, pp. 17-22, 2005.
[12] A. K. Nanda, H. Singh, N. Misra, P. Paul, “Reliability properties of reversed residual lifetime”, Communications in Statistics-Theory and Methods, vol. 32, pp. 2031-2042, 2003.
[13] M. M. Nassar, F. H. Eissa, “On the exponentiated Weibull distribution”, Communications in Statistics-Theory and Methods, vol. 32, pp. 1317-1336, 2003.
[14] R. Tahmasbi, S. Rezaei, “A two-parameter lifetime distribution with decreasing failure rate”, Computational Statistics and Data Analysis, vol. 52, pp. 3889-3901, 2008.
[15] D. F. Andrews, A. M. Herzberg, “Data: A Collection of Problems from Many Fields for the Student and Research Worker”, Springer Series in Statistics, New York, 1985.
[16] L. Kamberi, T. Iljazi, S. Orhani, “Statistical Analysis on Information Technology Impact in Quality Learning of Mathematics (for Grades VI-IX)”, Journal of Natural Sciences and Mathematics of UT, vol. 6, no. 11-12, pp. 123-134, 2021.
[17] F. Merovci, I. Elbatal, “Weibull Rayleigh Distribution: Theory and Applications”, Appl. Math. Inf. Sci. Vol. 9, no. 4, pp. 2127-2137, 2015.