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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
Volume 6, Issue 5, October 2020, Pages: 137-144
Received: Sep. 29, 2020; Accepted: Oct. 14, 2020; Published: Oct. 21, 2020
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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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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.
Zero-Inflation, Dispersion, Insurance Claims, Poisson Distributions
To cite this article
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, International Journal of Data Science and Analysis. Vol. 6, No. 5, 2020, pp. 137-144. doi: 10.11648/j.ijdsa.20200605.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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