Orthogonal polynomials for tailoring density functions to excess kurtosis, asymmetry and dependence

Followiong on a reappraisal of othogonal-polynomial role in characterizing a distribution, this paper investigates the issue of how to tailor distributions to embody evidence of moments and dependance behaviours deviating from theoretic instances. As the paper shows, the orthogonal polynomials associated with a distribution clear the way to reshaping distributions so as to encode information on extra kurtosis, and between-squares dependence. Operational conditions of positive definiteness of modified distributions are duly provided.