A New Two-Component Hybrid Model for Highly Right-Skewed Data: Estimation Algorithm and Application to Rainfall Data from South Tyrol, Italy

In many real-life processes, data with high positive skewness are very common. Moreover, these data tend to exhibit heterogeneous characteristics in such a manner that using one parametric univariate probability distribution becomes inadequate to model such data. When the heterogeneity of such data can be appropriately separated into two components—the main innovation component, where the bulk of data is centered, and the tail component which contains some few extreme observations—in such a way, and without a loss in generality, that the data possesses high skewness to the right, the use of hybrid models to model the data becomes very viable. In this paper, a new two-component hybrid model which combines the half-normal distribution for the main innovation of a positive and highly right-skewed data with the generalized Pareto distribution (GPD) for the observations in the data above a certain threshold is proposed. To enhance efficiency in the estimation of the parameters of the hybrid model, an unsupervised iterative algorithm (UIA) is adopted. The hybrid model is applied to model the intensity of rainfall which triggered some debris flow events in the South Tyrol region of Italy. Results from Monte Carlo simulations, as well as from the model’s application to the real data, clearly show how the UIA enhances the estimation of the free parameters of the hybrid model to offer good fits to positive and highly right-skewed data. Application results of the hybrid model are also compared with the results of other two-component hybrid models and graphical threshold selection methodologies in extreme value theory.