International Journal of Statistical Distributions and Applications

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Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims

Received: 01 March 2017    Accepted: 08 May 2017    Published: 07 December 2017
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Abstract

The aim of this study is to determine the best mixture model for claim amount from a comprehensive insurance policy portfolio and use the model to estimate the expected claim amount per risk for the coming calendar year. The claims data were obtained from the motor insurance office of one of the top business insurance companies in Ghana. The data consists of one thousand (1,000) claim amounts from January 2012 to December 2014. The expectation-maximization (EM) algorithm within a maximum likelihood framework was used to estimate the parameters of four mixture models namely the Heterogeneous Normal-Normal, Homogeneous Normal-Normal, Pareto-Gamma and Gamma-Gamma. These mixture models were fitted to the claims data and measures of goodness-of-fit (AIC and BIC) were used to determine the best mixture model. The Heterogeneous Normal-Normal mixture distribution was the appropriate model for the motor insurance claims data due to the least AIC. The estimated expected claims amount for the coming calendar year (2015) from the model was GHS 877.672 per risk. This in a way may inform decision makers as to the kind of anticipated reserves for future claims.

DOI 10.11648/j.ijsd.20170304.19
Published in International Journal of Statistical Distributions and Applications (Volume 3, Issue 4, December 2017)
Page(s) 124-128
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

EM Algorithm, Maximum Likelihood, Finite Mixture, Comprehensive Insurance Policy, AIC

References
[1] Finite Mixture Models. By Geoffrey McLachlan and David Peel. Copyright 2000 John Wiley & Sons, Inc. ISBN: 0-471-00626-2.
[2] Teodorescu, S. (2009). Loss distributions modeling for motor tpl insurance class using Gaussian mixture method and EM algorithm.
[3] Hogg, R. V. and Klugman, S. A. (2008). Modeling Loss Distributions. John Wiley Sons, New York.
[4] Janczuraa, J. and Weron, R. (2010). An empirical comparison of alternate regime-switching models for electricity spot prices. MPRA.
[5] Dempster A, Laird N, Rubin D (1977). “Maximum Likelihood from Incomplete Data via the EM-Alogrithm.” Journal of the Royal Statistical Society, B, 39, 1–38.
[6] Hewitt, C. J. and Leftkowitz, B. (1979). Methods for fitting distributions to insurance loss data. Proc. Casualty Actuarial Science Soc.
[7] Davenport, J., Bezdek, J., and Hathaway, R. (1988). Parameter estimation for finite mixture distributions. Comput. Math. Applica., 15, No. 10: 819–828.
[8] McLachlan, G. and Peel, D. (2008). Finite Mixture Models. John Wiley Sons, Inc., New York.
[9] Atienza, N., Garcia-Heras, J., and Munoz-Pichardo, J. (2006). A new condition for identifiability of finite mixture distributions. Research Gate.
[10] Zhang, L., Gove, J. H., Liu, C., and Leak, W. B. (2001). A finite mixture of two weibull distributions for modeling the diameter distribtuons of rotated-sigmoid, uneven-aged stands. Canadian Journal of Forest Research, 31.
[11] Zhang, H. and Huang, Y. (2015). Finite mixture models and their applications: A review. Austin Biometrics and Biostatistics.
[12] Sattayatham, P. and Talangtam, T. (2012). Fitting of finite mixture distributions to motor insurance claims. Journal of Mathematics and Statistics 8(1): 49-56, ISSN 154-3644.
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Author Information
  • Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

  • Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

  • Faculty of Engineering, Ghana Technology University College, Kumasi, Ghana

  • Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

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    Nana Kena Frempong, Osei Tawiah Owusu, Maxwell Akwasi Boateng, Francis Kwame Bukari. (2017). Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims. International Journal of Statistical Distributions and Applications, 3(4), 124-128. https://doi.org/10.11648/j.ijsd.20170304.19

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    ACS Style

    Nana Kena Frempong; Osei Tawiah Owusu; Maxwell Akwasi Boateng; Francis Kwame Bukari. Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims. Int. J. Stat. Distrib. Appl. 2017, 3(4), 124-128. doi: 10.11648/j.ijsd.20170304.19

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    AMA Style

    Nana Kena Frempong, Osei Tawiah Owusu, Maxwell Akwasi Boateng, Francis Kwame Bukari. Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims. Int J Stat Distrib Appl. 2017;3(4):124-128. doi: 10.11648/j.ijsd.20170304.19

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  • @article{10.11648/j.ijsd.20170304.19,
      author = {Nana Kena Frempong and Osei Tawiah Owusu and Maxwell Akwasi Boateng and Francis Kwame Bukari},
      title = {Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims},
      journal = {International Journal of Statistical Distributions and Applications},
      volume = {3},
      number = {4},
      pages = {124-128},
      doi = {10.11648/j.ijsd.20170304.19},
      url = {https://doi.org/10.11648/j.ijsd.20170304.19},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijsd.20170304.19},
      abstract = {The aim of this study is to determine the best mixture model for claim amount from a comprehensive insurance policy portfolio and use the model to estimate the expected claim amount per risk for the coming calendar year. The claims data were obtained from the motor insurance office of one of the top business insurance companies in Ghana. The data consists of one thousand (1,000) claim amounts from January 2012 to December 2014. The expectation-maximization (EM) algorithm within a maximum likelihood framework was used to estimate the parameters of four mixture models namely the Heterogeneous Normal-Normal, Homogeneous Normal-Normal, Pareto-Gamma and Gamma-Gamma. These mixture models were fitted to the claims data and measures of goodness-of-fit (AIC and BIC) were used to determine the best mixture model. The Heterogeneous Normal-Normal mixture distribution was the appropriate model for the motor insurance claims data due to the least AIC. The estimated expected claims amount for the coming calendar year (2015) from the model was GHS 877.672 per risk. This in a way may inform decision makers as to the kind of anticipated reserves for future claims.},
     year = {2017}
    }
    

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    T1  - Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims
    AU  - Nana Kena Frempong
    AU  - Osei Tawiah Owusu
    AU  - Maxwell Akwasi Boateng
    AU  - Francis Kwame Bukari
    Y1  - 2017/12/07
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    DO  - 10.11648/j.ijsd.20170304.19
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    JF  - International Journal of Statistical Distributions and Applications
    JO  - International Journal of Statistical Distributions and Applications
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    EP  - 128
    PB  - Science Publishing Group
    SN  - 2472-3509
    UR  - https://doi.org/10.11648/j.ijsd.20170304.19
    AB  - The aim of this study is to determine the best mixture model for claim amount from a comprehensive insurance policy portfolio and use the model to estimate the expected claim amount per risk for the coming calendar year. The claims data were obtained from the motor insurance office of one of the top business insurance companies in Ghana. The data consists of one thousand (1,000) claim amounts from January 2012 to December 2014. The expectation-maximization (EM) algorithm within a maximum likelihood framework was used to estimate the parameters of four mixture models namely the Heterogeneous Normal-Normal, Homogeneous Normal-Normal, Pareto-Gamma and Gamma-Gamma. These mixture models were fitted to the claims data and measures of goodness-of-fit (AIC and BIC) were used to determine the best mixture model. The Heterogeneous Normal-Normal mixture distribution was the appropriate model for the motor insurance claims data due to the least AIC. The estimated expected claims amount for the coming calendar year (2015) from the model was GHS 877.672 per risk. This in a way may inform decision makers as to the kind of anticipated reserves for future claims.
    VL  - 3
    IS  - 4
    ER  - 

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