Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions

Punzo, Antonio, Mazza, Angelo and Maruotti, Antonello (2018) Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions. Journal of Applied Statistics, 1-22. (doi:10.1080/02664763.2018.1428288).

Abstract

Insurance and economic data are frequently characterized by positivity, skewness, leptokurtosis, and multi-modality; although many parametric models have been used in the literature, often these peculiarities call for more flexible approaches. Here, we propose a finite mixture of contaminated gamma distributions that provides a better characterization of data. It is placed in between parametric and non-parametric density estimation and strikes a balance between these alternatives, as a large class of densities can be implemented. We adopt a maximum likelihood approach to estimate the model parameters, providing the likelihood and the expected-maximization algorithm implemented to estimate all unknown parameters. We apply our approach to an artificial dataset and to two well-known datasets as the workers compensation data and the healthcare expenditure data taken from the medical expenditure panel survey. The Value-at-Risk is evaluated and comparisons with other benchmark models are provided.

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