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Dichotomous unimodal compound models: application to the distribution of insurance losses

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  • Salvatore D. Tomarchio
  • Antonio Punzo

Abstract

A correct modelization of the insurance losses distribution is crucial in the insurance industry. This distribution is generally highly positively skewed, unimodal hump-shaped, and with a heavy right tail. Compound models are a profitable way to accommodate situations in which some of the probability masses are shifted to the tails of the distribution. Therefore, in this work, a general approach to compound unimodal hump-shaped distributions with a mixing dichotomous distribution is introduced. A 2-parameter unimodal hump-shaped distribution, defined on a positive support, is considered and reparametrized with respect to the mode and to another parameter related to the distribution variability. The compound is performed by scaling the latter parameter by means of a dichotomous mixing distribution that governs the tail behavior of the resulting model. The proposed model can also allow for automatic detection of typical and atypical losses via a simple procedure based on maximum a posteriori probabilities. Unimodal gamma and log-normal are considered as examples of unimodal hump-shaped distributions. The resulting models are firstly evaluated in a sensitivity study and then fitted to two real insurance loss datasets, along with several well-known competitors. Likelihood-based information criteria and risk measures are used to compare the models.

Suggested Citation

  • Salvatore D. Tomarchio & Antonio Punzo, 2020. "Dichotomous unimodal compound models: application to the distribution of insurance losses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2328-2353, November.
  • Handle: RePEc:taf:japsta:v:47:y:2020:i:13-15:p:2328-2353
    DOI: 10.1080/02664763.2020.1789076
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    Cited by:

    1. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    2. Amovin-Assagba, Martial & Gannaz, Irène & Jacques, Julien, 2022. "Outlier detection in multivariate functional data through a contaminated mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    3. Punzo, Antonio & Bagnato, Luca, 2021. "Modeling the cryptocurrency return distribution via Laplace scale mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    4. Tortora, Cristina & Franczak, Brian C. & Bagnato, Luca & Punzo, Antonio, 2024. "A Laplace-based model with flexible tail behavior," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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