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Cited by 12 publications
(8 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: Discussionmentioning
confidence: 65%
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: Discussionmentioning
confidence: 65%
“…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%
“…In this connection let us introduce the following. x j f (x)dx (50) (see Faliva et al (2016) for details).…”
Section: Resultsmentioning
confidence: 99%
“…In the Gaussian case, these polynomials are the Hermite ones and the polynomially modified density is known as Gram-Charlier expansion. This approach is particularly interesting because it can be tailored on the specific features of the empirical distribution at hand and can be extended to other distributions besides the normal one (see Faliva et al (2016)). This paper develops the approach further so as to obtain the densities of sums of leptokurtic normal random variables with same or different kurtosis.…”
Section: Introductionmentioning
confidence: 99%
“…A similar approach can be applied to reshape any multivariate elliptical distribution in order to obtain a more general elliptical distribution with the desired amount of excess kurtosis. Note that a first attempt to use orthogonal polynomials in the multivariate context has been made in Faliva, Zoia, & Poti (). Nevertheless the authors define multivariate distributions in the time series context and they use a pairwise approach: multivariate dependencies are defined on successive pairs of variables only (see formula (4.24) of the cited paper).…”
Section: The Mln Distributionmentioning
confidence: 99%