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Using Genetic Algorithms for Parameter Estimation of a Two-Component Circular Mixture Model

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4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019) (CMES 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1111))

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Abstract

In many engineering and biological applications, the data sets such as wave direction, orientations of animal are circular. This type of data refers as circular data and cannot be analyzed using linear statistical methods. The most common distributions for analyzing circular data are the von Mises (vM) and wrapped Cauchy (wC) distributions. In the present chapter, we consider a two-component circular mixture model of the vM and wC distributions. In order to obtain the maximum likelihood estimators of the parameters of the circular mixture model, we consider four optimization methods as the Newton-Raphson, Nelder-Mead, simulated annealing and the proposed genetic algorithm (GA). Here, GAs are a class of evolutionary algorithms and based on the principles of biological systems. The search space in GA addresses for the circular mixture model. To compare the performance of four optimization methods, we present the simulation study and phase data examples. The results indicate that the proposed GA seems to perform well in terms of parameter estimations as seen in simulated and phase data examples.

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Authors and Affiliations

  1. Department of Business Administration, Burdur Mehmet Akif Ersoy University, Burdur, Turkey

    Muhammet Burak Kılıç

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  1. Muhammet Burak Kılıç
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Correspondence to Muhammet Burak Kılıç .

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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. FSTE, Moulay Ismail University, Meknes, Morocco

    Zakia Hammouch

  3. Department of Mathematics, Fırat University, Elâzığ Merkez, Turkey

    Hasan Bulut

  4. Faculty of Education, Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey

    Haci Mehmet Baskonus

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Kılıç, M.B. (2020). Using Genetic Algorithms for Parameter Estimation of a Two-Component Circular Mixture Model. In: Dutta, H., Hammouch, Z., Bulut, H., Baskonus, H. (eds) 4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019). CMES 2019. Advances in Intelligent Systems and Computing, vol 1111. Springer, Cham. https://doi.org/10.1007/978-3-030-39112-6_6

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  • DOI: https://doi.org/10.1007/978-3-030-39112-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39111-9

  • Online ISBN: 978-3-030-39112-6

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