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A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems

Author

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  • Payandeh Najafabadi Amir T.

    (Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran)

  • MohammadPour Saeed

    (Headquarters of Iran Insurance Company, Tehran, Iran)

Abstract

This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model’s parameters. Then, such new model along with a Pareto mixture model have employed to design an optimal rate–making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated Negative Binomial mixture distribution/regression model as well as other well developed counting models along with a Pareto mixture model to model frequency/severity of reported claims in Iranian third party insurance dataset. Such numerical illustration shows that: (1) the k-Inflated Negative Binomial mixture models provide more fair rate/pure premiums for policyholders under a rate–making system; and (2) in the situation that number of reported claims uniformly distributed in past experience of a policyholder (for instance k1=1$k_1=1$ and k2=1$k_2=1$ instead of k1=0$k_1=0$ and k2=2$k_2=2$). The rate/pure premium under the k-Inflated Negative Binomial mixture models are more appealing and acceptable.

Suggested Citation

  • Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
  • Handle: RePEc:bpj:apjrin:v:12:y:2018:i:2:p:31:n:2
    DOI: 10.1515/apjri-2017-0014
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    References listed on IDEAS

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    Cited by:

    1. Shengkun Xie & Anna T. Lawniczak, 2018. "Estimating Major Risk Factor Relativities in Rate Filings Using Generalized Linear Models," IJFS, MDPI, vol. 6(4), pages 1-14, October.

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