Comparison of estimation methods for the Kumaraswamy Weibull distribution

Year 2023, Volume: 72 Issue: 1, 1 - 21, 30.03.2023

Cansu Ergenç , Birdal Şenoğlu

https://doi.org/10.31801/cfsuasmas.1086966

Abstract

In this study, the performances of the different parameter estimation methods are compared for the Kumaraswamy Weibull distribution via Monte Carlo simulation study. Maximum Likelihood (ML), Least Squares (LS), Weighted Least Squares (WLS), Cramer-von Mises (CM) and Anderson Darling (AD) methods are used in the comparisons. The results of the Monte Carlo simulation study demonstrate that ML estimators for the parameters of the Kumaraswamy Weibull distribution are more efficient than the other estimators. It is followed by AD estimator. At the end of the study, a real data set taken from the literature is used to illustrate the applicability of the Kumaraswamy Weibull distribution.

Keywords

KwWeibull distribution, Weibull distribution, estimation methods, Monte Carlo simulation, efficiency

References

• Acitas, S., Senoglu, B., Robust factorial ANCOVA with LTS error distributions, Hacet. J. Math. Stat., 47(2) (2018), 347-363. https://doi.org/10.15672/HJMS.201612918797
• Akgül, F. G., Şenoğlu, B., Arslan, T., An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution, Energy Convers. Manag., 114 (2016), 234-240. https://doi.org/10.1016/j.enconman.2016.02.026
• Bowman, K. O., Shenton, L. R., Weibull distributions when the shape parameter is defined, Comput Stat Data Anal, 36(3) (2001), 299-310. https://doi.org/10.1016/S0167-9473(00)00048-7
• Calabria, R., Pulcini, G., An engineering approach to Bayes estimation for the Weibull distribution, Microelectron. Reliab., 34(5) (1994), 789-802. https://doi.org/10.1016/0026-2714(94)90004-3
• Cordeiro, G. M., de Castro, M., A new family of generalized distributions, J. Stat. Comput. Simul., 81(7) (2011), 883-898. https://doi.org/10.1080/00949650903530745
• Cordeiro, G. M., Ortega, E. M., Nadarajah, S., The Kumaraswamy Weibull distribution with application to failure data, J Franklin Inst, 347(8) (2010), 1399-1429. https://doi.org/10.1016/j.jfranklin.2010.06.010
• Cortez, P., Morais, A. D. J. R., A data mining approach to predict forest fires using meteorological data, New Trends in Artificial Intelligence: Proceedings of the 13th Portuguese Conference on Artificial Intelligence, Guimaraes, Portugal, (2007), 512-523.
• Elbatal, I., Diab, L. S., Alim, N. A., Transmuted generalized linear exponential distribution, Int. J. Comput. Appl., 83(17) (2013), 29-37. https://doi.org/10.1515/eqc-2013-0020
• Elbatal, I., Elgarhy, M., Statistical properties of Kumaraswamy quasi Lindley distribution, IJMTT, 4(10) (2013), 237-246.
• Ergenç, C., Statistical Inference for Some Non-Normal Distributions, Master Thesis, Ankara University, 2021.
• Eugene, N., Lee, C., Famoye, F., Beta-normal distribution and its applications, Commun. Stat. Theory Methods, 31(4) (2002), 497-512. https://doi.org/10.1081/STA-120003130
• Gomes, A. E., da-Silva, C. Q., Cordeiro, G. M., Ortega, E. M., A new lifetime model: the Kumaraswamy generalized Rayleigh distribution, J. Stat. Comput. Simul., 84(2) (2014), 290-309. https://doi.org/10.1080/00949655.2012.706813
• Islam, M. Q., Tiku, M. L., Multiple linear regression model under nonnormality, Commun. Stat. Theory Methods, 33(10) (2005), 2443-2467. https://doi.org/10.1081/STA-200031519
• Jones, M. C., Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages, Stat. Methodol., 6 (2008), 70–81. https://doi.org/10.1016/j.stamet.2008.04.001
• Kantar, Y. M., Şenoğlu, B., A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter, Comput Geosci, 34(12) (2008), 1900-1909. https://doi.org/10.1016/j.cageo.2008.04.004
• Keats, J. B., Lawrence, F. R., Wang, F. K., Weibull maximum likelihood parameter estimates with censored data, J. Qual. Technol., 29(1) (1997), 105-110. https://doi.org/10.1080/00224065.1997.11979730
• Maurya, S. K., Singh, S. K., Singh, U., A new right-skewed upside down bathtub shaped heavytailed distribution and its applications, J. Mod. Appl. Stat. Methods, 19(1) (2020), eP2888. https://doi.org/10.22237/jmasm/1608552600
• Mudholkar, G. S., Srivastava, D. K., Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Reliab., 42(2) (1993), 299-302.
• Rocha, R., Nadarajah, S., Tomazella, V., Louzada, F., Eudes, A., New defective models based on the Kumaraswamy family of distributions with application to cancer data sets, Stat Methods Med Res, 26(4) (2017), 1737-1755. https://doi.org/10.1177/0962280215587976
• Saeed, M. K., Salam, A., Rehman, A. U., Saeed, M. A., Comparison of six different methods of Weibull distribution for wind power assessment: A case study for a site in the Northern region of Pakistan, Sustain. Energy Technol. Assess., 36 (2019), 100541. https://doi.org/10.1016/j.seta.2019.100541
• Sarhan, A. M., Zaindin, M., Modified Weibull distribution, APPS. Applied Sciences, 11 (2009), 123-136.
• Serban, A., Paraschiv, L. S., Paraschiv, S., Assessment of wind energy potential based on Weibull and Rayleigh distribution models, Energy Rep., 6 (2020), 250-267. https://doi.org/10.1016/j.egyr.2020.08.048
• Swain, J. J., Venkatraman, S., Wilson, J. R., Least-squares estimation of distribution functions in Johnson’s translation system, J Stat Comput Simul, 29(4) (1988), 271-297. https://doi.org/10.1080/00949658808811068
• Wolfowitz, J., Estimation by the minimum distance method in nonparametric stochastic difference equations, Ann. Math. Stat., 25(2) (1954), 203-217. http://www.jstor.org/stable/2236727
• Wolfowitz, J., Estimation by the minimum distance method, Ann Inst Stat Math, 5(1) (1953), 9-23.