Orthogonal polynomials for tailoring density functions to excess kurtosis, asymmetry, and dependence
Valerio Potì () and
Maria Zoia ()
Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 1, 49-62
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.
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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:1:p:49-62
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