A new two-component hybrid model for highly right-skewed data: estimation algorithm and application to finance and rainfall data

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 becomes very viable to model the data. In this paper, we propose a new two-component hybrid model which joins the half-normal distribution for the main innovation of a highly right-skewed data with the generalized Pareto distribution (GPD) for the observations in the data above a certain threshold. To enhance efficiency in the estimation of the parameters of the hybrid model, an unsupervised iterative algorithm (UIA) is adopted. An application of the hybrid model in modeling the absolute log returns of the S&P500 index and the intensity of rainfall which triggered some debris flow events in the South Tyrol region of Italy is carried out.