A data transformation for the estimation of decay types of multivariate distributions

A transformation of unimodal multivariate data is introduced for increased precision in the estimation of the exponential decay type of the underlying density. The transformation renders the contour lines of the probability density function more uniformly spherical and enables conservation of unimodality, without assuming the ability to efficiently estimate the mode's location. The concept of transformation is extended to the case of non-modal center-points, for which the conservation of unimodality is non-trivial. This paper presents a discussion of the estimation procedure of exponential decay types under skewness and preservation of the unimodal quality. (C) 2020 The Authors. Published by Elsevier B. V.