The Simplicial Generelized Beta distribution - R-package SGB and applications

The simplex is the geometrical locus of D-dimensional positive data with constant sum, called compositions.  When modeling compositions, the well established strategy is to get rid of the constraint by applying a log-ratio transform (lrt) of the parts (elements of the composition). The Dirichlet distribution is a generalization of the Beta distribution to D > 2 parts. It depends on D shape parameters. A generalization of the Dirichlet, called the Simplicial Generalized Beta (SGB) distribution (Graf, 2017), encompass an overall shape parameter, a scale composition and the D Dirichlet shapes. The SGB is flexible enough to accommodate many practical situations.

In this talk, models based on a the SGB will be presented. SGB regression models will be applied to two examples, one is the modeling of automobile segment shares data (Morais and Thomas-Agnan, 2019) and the other is the United Kingdom Time Use Survey (Gershuny and Sullivan, 2017). The R-package SGB (Graf, 2019) will make the methods accessible to users.