Quadratic Transformations of Copula Density and Probability Density

Pharunyou Chanthorn

Abstract

Studying transformations is a simple way to obtain   new types of mappings in data analysis.   In this work,  we  present   a characterization of  quadratic transformations  of copula densities.  Additionally,  we also characterize quadratic transformations  of probability densities.Both transformations  correspond to  their  quadratic  coefficients  and the sets  of      their     coefficients  are always convex. Especially,   the  set  of         coefficients   of quadratic transformations  of probability densities   is a non-polygon.