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Cited by 18 publications
(17 citation statements)
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“…This paper extends recent insights (see [3,5,6]) on the issue of tailoring distributions in order to account for over-kurtosis. Starting from a given spherical distribution, the orthogonal polynomials of its related modular variable are provided and used to design the intended distribution shape adapter.…”
Section: Discussionsupporting
confidence: 61%
See 1 more Smart Citation
“…This paper extends recent insights (see [3,5,6]) on the issue of tailoring distributions in order to account for over-kurtosis. Starting from a given spherical distribution, the orthogonal polynomials of its related modular variable are provided and used to design the intended distribution shape adapter.…”
Section: Discussionsupporting
confidence: 61%
“…So far, this method-which can be viewed as an inheritance of the Gram-Charlier expansion-has proved effective when applied to distributions to account for possibly severe kurtosis and skewness (e.g., [5,6]). In this paper, we gain further insight into the matter and work out a similar orthogonal-polynomial-based approach to increasing the values of the moments-in particular, the fourth-within a multivariate spherical framework.…”
Section: Introductionmentioning
confidence: 99%
“…This latter approach, which has the advantage of allowing for greater flexibility in fitting empirical distributions, is the one we have followed in this paper. Recently, Zoia (2010); Bagnato et al (2015)) have proposed a method to account for excess kurtosis of a density based on its polynomial transformation through its associated orthogonal polynomials. In the Gaussian case, these polynomials are the Hermite ones and the polynomially modified density is known as Gram-Charlier expansion.…”
Section: Introductionmentioning
confidence: 99%
“…For a given set of basis functions, a different ordering will generate a different set of polynomials. We use the basis functions x n = x n 1 1 • • • x n q q . But others are sometimes appropriate: see Withers (2009) for an example.…”
Section: Introductionmentioning
confidence: 99%