Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya

Polycarp Nyabuto; Anthony Wanjoya; Antony Ngunyi

doi:doi:10.11648/j.ijdsa.20200605.13

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Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya

Polycarp Nyabuto, Anthony Wanjoya, Antony Ngunyi

Published in International Journal of Data Science and Analysis (Volume 6, Issue 5)

Received: 29 September 2020 Accepted: 14 October 2020 Published: 21 October 2020

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Abstract

The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.

Published in	International Journal of Data Science and Analysis (Volume 6, Issue 5)
DOI	10.11648/j.ijdsa.20200605.13
Page(s)	137-144
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), 2020. Published by Science Publishing Group

Keywords

Zero-Inflation, Dispersion, Insurance Claims, Poisson Distributions

References

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[3]	Insurance Regulatory Authority. (2017). Insurance Annual Report. Nairobi: Insurance Regulatory Authority. https://www.ira.go.ke.
[4]	Edward, W. F., Gee, Lee. & Lu, Yang. (2016). Multivariate Frequency-Severity Regression models in Insurance. Department of Statistics, University of Wisconsin-Madison, 1300 University Avenue, Madison, WI 53706, USA.
[5]	Feldman, J. A., & Robert, L. B. (2005). Risk and Insurance. Education and Examination Committee for the Society of Actuaries. https://www.soa.org/globalassets/assets/files/edu/P-21-05.pdf.
[6]	Kwame, G. A., ELVIS, D., & Agbodah, K. (2014). Probability Modeling and Simulation of Insurance Claims in Ghana. Global Journal of Commerce and Management Perspective, 3 (5); 41-49. ISSN 2319-7285.
[7]	Yulia, R., Noriszura, I., & Saiful, H. J. (2013). Estimation of Claim Cost Data Using Zero Adjusted Gamma and Inverse Gaussian Regression Models. Journal of Mathematics and Statistics, 9 (3); 186-192. doi: 10.3844/jmssp.2013.186.192.
[8]	Vytaras, B., & Andreas, K. (2015). Measuring Severity and Tail Risk of Norwegian Fire Insurance Claims. North American Actuarial Journal, 20 (1); 1-16. doi: 10.1080/10920277.2015.1062784.
[9]	Joseph, N. W., & Christophe, P. (2011). On the Zero-Inflated Count Models with Application to Modeling Annual trends in Incidences of some Occupational Allergic Diseases in France. Journal of Data Science 9 (2011); 639-659.
[10]	Rotimi, F. A., Oyindamola B. Y., & Ayoola S. A. (2018). Modeling excess zeros in count data with application to Antenatal Care Utilization. International Journal of Statistics and Probability, 7 (3); 22-35. Doi: 105539/ijsp.v7n3p22.
[11]	Marjan, Q. (2019). On the Violation of Claims with Excess Zeros in Liability Insurance: A comparative study. Open access journal, 7 (3); 1-17.
[12]	Evgenii, V. G., & Elena, A. M. (2017). Modern Claim frequency and severity models: An application to the Russian motor and own damage insurance market. Cogent Economics & Finance, 5 (1). doi: 10.1080/23322039.2017.1311097.
[13]	Sakthivel, K. M., & Rajitha, C. S. (2017). A Comparative Study of Zero-Inflated, Hurdle Models with Artificial Neural Network in Claim Count Modeling. International Journal of Statistics and Systems, 12 (2); 265-276. ISSN 0973-2675.
[14]	Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2Nd Edition). Advanced series on statistical science & applied probability, 14 (2); World Scientific Publishing Co. ISBN-13: 978-9813203617.
[15]	Staub, k., & Winkelmann, R. (2013). Consistent estimation of zero inflated count models. Health Economics, (22); 673-686. doi: 10.1002/hec.2844.
[16]	Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2008). Loss Models: From Data to Decisions (Thirded.) John Wiley & Sons, Inc. ISBN: 978-1-119-52378-9.
[17]	Cheng Tian. (2018). Hurdle Models in Non-Life Insurance. Foculty of Mathematics and Physics, Charles University. Thesis Id: 188550.

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APA Style

Polycarp Nyabuto, Anthony Wanjoya, Antony Ngunyi. (2020). Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. International Journal of Data Science and Analysis, 6(5), 137-144. https://doi.org/10.11648/j.ijdsa.20200605.13

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ACS Style

Polycarp Nyabuto; Anthony Wanjoya; Antony Ngunyi. Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. Int. J. Data Sci. Anal. 2020, 6(5), 137-144. doi: 10.11648/j.ijdsa.20200605.13

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AMA Style

Polycarp Nyabuto, Anthony Wanjoya, Antony Ngunyi. Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. Int J Data Sci Anal. 2020;6(5):137-144. doi: 10.11648/j.ijdsa.20200605.13

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@article{10.11648/j.ijdsa.20200605.13,
  author = {Polycarp Nyabuto and Anthony Wanjoya and Antony Ngunyi},
  title = {Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {5},
  pages = {137-144},
  doi = {10.11648/j.ijdsa.20200605.13},
  url = {https://doi.org/10.11648/j.ijdsa.20200605.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200605.13},
  abstract = {The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.},
 year = {2020}
}

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TY  - JOUR
T1  - Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya
AU  - Polycarp Nyabuto
AU  - Anthony Wanjoya
AU  - Antony Ngunyi
Y1  - 2020/10/21
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200605.13
DO  - 10.11648/j.ijdsa.20200605.13
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 137
EP  - 144
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200605.13
AB  - The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.
VL  - 6
IS  - 5
ER  -

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Author Information

Polycarp Nyabuto

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya
Antony Ngunyi

Department of Statistics and Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya

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APA Style

Polycarp Nyabuto, Anthony Wanjoya, Antony Ngunyi. (2020). Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. International Journal of Data Science and Analysis, 6(5), 137-144. https://doi.org/10.11648/j.ijdsa.20200605.13

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ACS Style

Polycarp Nyabuto; Anthony Wanjoya; Antony Ngunyi. Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. Int. J. Data Sci. Anal. 2020, 6(5), 137-144. doi: 10.11648/j.ijdsa.20200605.13

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AMA Style

Polycarp Nyabuto, Anthony Wanjoya, Antony Ngunyi. Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya. Int J Data Sci Anal. 2020;6(5):137-144. doi: 10.11648/j.ijdsa.20200605.13

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@article{10.11648/j.ijdsa.20200605.13,
  author = {Polycarp Nyabuto and Anthony Wanjoya and Antony Ngunyi},
  title = {Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya},
  journal = {International Journal of Data Science and Analysis},
  volume = {6},
  number = {5},
  pages = {137-144},
  doi = {10.11648/j.ijdsa.20200605.13},
  url = {https://doi.org/10.11648/j.ijdsa.20200605.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20200605.13},
  abstract = {The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.},
 year = {2020}
}

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TY  - JOUR
T1  - Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya
AU  - Polycarp Nyabuto
AU  - Anthony Wanjoya
AU  - Antony Ngunyi
Y1  - 2020/10/21
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdsa.20200605.13
DO  - 10.11648/j.ijdsa.20200605.13
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 137
EP  - 144
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20200605.13
AB  - The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.
VL  - 6
IS  - 5
ER  -

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