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

M. Faliva, Valerio Potì () and Maria Zoia ()

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 1, 49-62

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.

Date: 2016
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DOI: 10.1080/03610926.2013.818698

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