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

• Published in: Journal of applied statistics Vol. 45; no. 14; pp. 2563 - 2584
• Main Authors: Punzo, Antonio, Mazza, Angelo, Maruotti, Antonello
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 26.10.2018; Taylor & Francis Ltd
• Subjects: Contaminated distributions; Economic models; Expenditures; finite mixtures; gamma distribution; Insurance; insurance claims; Mathematical models; Maximum likelihood estimates; Outliers (statistics); Parameter estimation; robust estimation; Statistical methods
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2018.1428288

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.