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.
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Acknowledgements
We would like to thank the editors and anonymous referees for valuable comments and insightful suggestions, which helped us to improve the manuscript. This work was supported by the Scientific Research Projects Coordination Unit of Burdur Mehmet Akif Ersoy University. Project Number 0440-DR-17.
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Comparison of the population sizes in terms of DEF criterion. Lowest values are indicated in red (colour figure online)
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Kılıç, M.B., Şahin, Y. & Koca, M.B. Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation. Comput Stat 36, 1219–1242 (2021). https://doi.org/10.1007/s00180-020-01044-5
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DOI: https://doi.org/10.1007/s00180-020-01044-5