Flexible Class of Skew‐Symmetric Distributions
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21 citations
Cites background from "Flexible Class of Skew‐Symmetric Di..."
...This class of functions leads to a family of densities of type (6) with a large variety of shapes, even for K = 2 only; see Ma & Genton (2004) for formal properties of this family, and for a set of graphical illustrations....
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21 citations
Cites background from "Flexible Class of Skew‐Symmetric Di..."
...Let u = (x − μ)/σ and consider the FGST model of order 3, which seems to provide enough flexibility to model unimodal and bimodal data (Ma and Genton, 2004):...
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...Let u = (x − μ)/σ and consider the FGST model of order 3, which seems to provide enough flexibility to model unimodal and bimodal data (Ma and Genton, 2004): g (x;μ, σ, ν, α0, α1) = ( 2 σ ) ft (u; ν) ( α0u + α1u3 ) , (18) where ft denotes the pdf of the t-distribution with ν degrees of freedom....
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...Gupta and Gupta (2004) studied the generalization of the basic model of Azzalini (1985), while Ma and Genton (2004) considered a flexible class of skew-symmetric distributions....
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21 citations
20 citations
Cites background from "Flexible Class of Skew‐Symmetric Di..."
...This result can be used to define what Ma and Genton (2004) called the FGSN distribution h.x; ξ, ω2, α, β/=2ω−1 φ ( x− ξ ω ) Φ { α ( x− ξ ω ) +β ( x− ξ ω )3} : .10/ They proved that PDF (10) may have at most two modes and noted that, in general, as the degree of the odd polynomial w.x/ in function…...
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...For instance, Ma and Genton (2004) described a ‘flexible generalized skew normal’ (FGSN) random variable in which the PDF is defined by adding a parameter to the skew normal PDF, which may then have two modes....
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...One interesting feature is that function (8) is unimodal (Ma and Genton, 2004)....
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20 citations
Cites background from "Flexible Class of Skew‐Symmetric Di..."
...This class of distributions, introduced by Ma and Genton (2004), can systematically model light tails, multimodality and skewness....
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References
2,470 citations
"Flexible Class of Skew‐Symmetric Di..." refers background or methods in this paper
...This representation has been used by Azzalini & Capitanio (2003) to define certain distributions by perturbation of symmetry....
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...For K = 1, the pdf is always unimodal as was already noted by Azzalini (1985) for the univariate skew-normal distribution....
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...The case K = 1 corresponds to Azzalini & Dalla Valle's (1996) bivariate skew-normal distribution, which cannot capture the bimodality....
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...For K ¼ 1, the pdf is always unimodal as was already noted by Azzalini (1985) for the univariate skew-normal distribution....
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...In particular, for ,il = ,B2 = /33 = & = 0, the pdf is exactly the bivariate skew-normal proposed by Azzalini & Dalla Valle (1996), and known to be unimodal (see Fig....
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"Flexible Class of Skew‐Symmetric Di..." refers background in this paper
...Finally, note that the stochastic representation of FSSdistributions follows from the stochastic representation of SS distributions described byWang et al. (2004), see also Azzalini & Capitanio (2003)....
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...Similarly, multivariate distributions such as skew-t (Branco & Dey, 2001; Azzalini & Capitanio, 2003; Jones & Faddy, 2003; Sahu et al., 2003), skew-Cauchy (Arnold & Beaver, 2000) and other skewelliptical ones (Azzalini & Capitanio, 1999; Branco & Dey, 2001; Sahu et al., 2003) can be represented by…...
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...Jones & Faddy (2003) and Azzalini & Capitanio (2003) fit two forms of skew-t distributions to these data....
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...If each term has an odd order (all ks are odd), then the polynomial is called an odd polynomial, whereas if each term has an even order (all ks are even), it is called an even polynomial....
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