Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims

Nana Kena Frempong; Osei Tawiah Owusu; Maxwell Akwasi Boateng; Francis Kwame Bukari

doi:doi:10.11648/j.ijsd.20170304.19

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Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims

Nana Kena Frempong, Osei Tawiah Owusu, Maxwell Akwasi Boateng, Francis Kwame Bukari

Published in International Journal of Statistical Distributions and Applications (Volume 3, Issue 4)

Received: 1 March 2017 Accepted: 8 May 2017 Published: 7 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.

Published in	International Journal of Statistical Distributions and Applications (Volume 3, Issue 4)
DOI	10.11648/j.ijsd.20170304.19
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), 2017. Published by Science Publishing Group

Keywords

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

References

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[3]	Hogg, R. V. and Klugman, S. A. (2008). Modeling Loss Distributions. John Wiley Sons, New York.
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[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.
[13]	Gong, Y. R. S. (1999). Gaussian mixture models.
[14]	Titterington, D., Smith, A., and Makov, U. (1985). Statistical Analysis of Finite Mixture Distributions. New Yok: Wiley.
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APA Style

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://article.sciencepublishinggroup.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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TY  - JOUR
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
PY  - 2017
N1  - https://doi.org/10.11648/j.ijsd.20170304.19
DO  - 10.11648/j.ijsd.20170304.19
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 124
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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Author Information

Nana Kena Frempong

Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Osei Tawiah Owusu

Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Maxwell Akwasi Boateng

Faculty of Engineering, Ghana Technology University College, Kumasi, Ghana
Francis Kwame Bukari

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

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Plain Text BibTeX RIS

APA Style

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

Copy | Download

@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://article.sciencepublishinggroup.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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TY  - JOUR
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
PY  - 2017
N1  - https://doi.org/10.11648/j.ijsd.20170304.19
DO  - 10.11648/j.ijsd.20170304.19
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 124
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  -

Copy | Download