Flexible Class of Skew‐Symmetric Distributions

By Yanyuan Ma, Marc G. Genton. 2004

193 citations recorded by the source corpus.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa6bbca9e98820268a919d37a105d20c0908695b

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Citations in the corpus

The multivariate skew-slash distribution (2006, background): “For instance, an odd polynomial of order three would yield a distribution that can model bimodality, see Ma and Genton (2004) for further discussions on this topic.”
On a class of two-piece skew-normal distributions (2005, methodology): “Other models, introduced by Ma and Genton [8] and Azzalini and Capitanio [9] to accommodate more than one mode, are obtained by developing flexible class of skew-symmetric distributions.”
Skew Brownian Motion and Pricing European Options (2007, background): “If the density of Y = UV is given by The density in (3) belongs to the skew-symmetric family of distributions of Ma and Genton (2004) , Wang et al .”
Robust Likelihood Methods Based on the Skew‐t and Related Distributions (2008, background): “One of these extensions refers to the family of flexible skew-symmetric (FSS) distributions introduced by Ma & Genton (2004) with density fFSS(x ; ξ, ω, α1, . . . , αK ) = 2ω−1 f0(z) G{PK (z)}, x ∈ R, (5) where f0 and G are symmetric univariate density function and distribution function,…”
A unified view on skewed distributions arising from selections (2006, methodology): “(24) Under regularity conditions on the pdffV, Ma & Genton (2004) have proved that the class of FSSdistributions is dense in the class ofSSdistributions under theL∞ norm.”
Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions (2005, unknown): “In fact, as shown by Ma and Genton (2004), π0(x) can be approximated arbitrarily well if we allow the order of the odd polynomial to increase sufficiently, and hence the estimator will approach the most efficient one.”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, methodology): “The use of odd polynomials for the function w has been proposed by Ma and Genton (2004) and leads to flexible skew-symmetric distributions that, in addition, can exhibit multimodality.”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “This important problem has been examined byWang et al. (2004) and Ma & Genton (2004), whose results can be summarized as follows; in their formulation, the term Gfw(x)g in (12) is replaced by the perturbation function p(x), satisfying conditions (14).”
Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions (2013, background): “…|−1/2tk(z0; )T (√ +k +‖z0‖2 ̄ T z0; +k ) , where as before z0 = −1/2(z − ), tk(x; ) is the tk(0, Ik , ) probability density function and T (x; +k) is the T1(0, 1, +k) cumulative distribution function; see Branco & Dey (2001), Azzalini & Capitanio (2003), Gupta (2003) and Ma & Genton (2004).”