Fitting a Hurdle Generalized Lambda Distribution to healthcare expenses
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In order to fit a model to healthcare expenses data, it is necessary to take into account some of its peculiarities, as the excess of zeros and its skewness, what demands flexible models instead of the usual ones from the exponential family. In this context, the Generalized Lambda Distribution (GLD) is quite useful, as it is highly flexible, for its parameters may be chosen in a way such that it has a given mean, variance, skewness and kurtosis. Furthermore, the GLD approximates very well other distributions, so that it may be employed as a wild-card distribution in many applications. Taking advantage of the GLD flexibility, we develop and apply to healthcare expenses data a hurdle, or two-way, model whose associated distribution is the GLD. We first present a thorough review of the literature about the GLD and then develop hurdle GLD marginal and regression models. Finally, we apply the developed models to a dataset consisting of yearly healthcare expenses, and model it in function of the covariates sex, age and previous year expenses. The fitted models are compared with the kernel density estimate and models based on the Generalised Pareto Distribution (GPD). It is established that the GLD models perform better than the GPD ones in modelling healthcare expenses.
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