Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull paramete
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Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation Muhammet Burak Kılıç1
1 · Yusuf Sahin ¸
· Melih Burak Koca1
Received: 30 July 2019 / Accepted: 22 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A mixture of two Weibull distributions (WW) has a variety of usage area from reliability analysis to wind speed modeling. Maximum likelihood (ML) method is the most frequently used method in parameter estimation of WW. Due to the nonlinear nature of the log-likelihood function of WW, usage of iterative techniques is a necessary process. Conventional iterative techniques such as Newton Raphson (NR) require considerable analytical preparatory to work to obtain gradient and may lead to numerical difficulties such as convergence problems. The aim of this paper is to present a genetic algorithm (GA) with an adaptive search space based on the Expectation— Maximization (EM) algorithm to obtain the ML estimators of the parameters of WW. The simulation study is conducted to compare the performances of ML estimators obtained using NR algorithm, EM algorithm, simulated annealing algorithm, and the proposed GA. Furthermore, real data examples are used to compare the efficiency of proposed GA with the existing methods in the literature. Simulation results and real data examples show that the proposed GA has superiority over other techniques in terms of efficiency. Keywords Weibull distribution · Finite mixture distributions · Bootstrap percentile interval
1 Introduction In many application fields, a single unimodal distribution may not be sufficient to model the data from populations known or suspected to include a number of subpopulations, in such cases, finite mixture models are useful (Everitt 1996). A mixture of two Weibull
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Melih Burak Koca [email protected] Department of Business Administration, Faculty of Economics and Administrative Sciences, Burdur Mehmet Akif Ersoy University, Burdur, Turkey
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distributions (WW) has been extensively studied to model a wide diversity of random phenomena such as lifetime of electron tubes (Kao 1959), survival times following cancer treatment (Chen et al. 1985), actual failures of the throttle for load-carrying vehicles (Jiang and Murthy 1995), wind speed occurrence at the heterogenous wind regimes (Jaramillo and Borja 2004; Carta and Ramirez 2007; Akda˘g et al. 2010; Kollu et al. 2012; Koca et al. 2019), daily rainfall amount (Suhaila and Jemain 2007), number of cycles to failure of electrical appliances (Elmahdy and Aboutahoun 2013; Erisoglu and Erisoglu 2018), failure times of oral irrigators (Karakoca et al. 2015), or aircraft engine failure (Yuan et al. 2018). In the context of WW parameter estimation, several methods have been employed such as graphical method, method of moments (MOM), method of logarithmic moments (MLM), maximum likelihood (ML) method, modified maximum likelihood method, least-squares method (LSM), L-moment method, perc
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