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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]