![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
This article deals with the problem of tailoring distributions to embody evidence of moments and dependence structure deviating from those of a given parent law. First, we show that finite-moment distributions can be reshaped, to allow for extra kurtosis, asymmetry, and dependence by using orthogonal polynomials. Then, we derive a set of orthogonal polynomials for adjusting any symmetric density to given requirements in terms of moments. Conditions for positiveness of the resulting polynomially modified distribution are further established. This provides a broader approach to reshaping parent distributions by means of polynomial adjustments than that currently found in the literature.