Quadratic transformations of copula density and probability density

Abstract

© 2019 by the Mathematical Association of Thailand. All rights reserved. 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.