Moments of skew-normal random vectors and their quadratic forms

By Marc G. Genton, Li He, Xiangwei Liu. 2001

153 citations recorded by the source corpus.

Subfields: Environmental Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e2d244af0c35de1ff73e4c364ef734995bd9b05c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Environmental Engineering

1. Philippe Naveau
2. Adelchi Azzalini
3. A. Capitanio
4. Marc G. Genton
5. Jing Wang
6. Arjun K. Gupta
7. Reinaldo Boris Arellano-Valle
8. Denis Allard

In Finance

1. Adelchi Azzalini
2. Marc G. Genton
3. Reinaldo Boris Arellano-Valle
4. A. Capitanio
5. Nicola Maria Rinaldo Loperfido
6. Victor Hugo Lachos
7. Jing Wang
8. Wen-Jang Huang

In Statistics and Probability

1. Adelchi Azzalini
2. Reinaldo Boris Arellano-Valle
3. Marc G. Genton
4. Victor Hugo Lachos
5. Heleno Bolfarine
6. Arjun K. Gupta
7. A. Capitanio
8. Wen-Jang Huang

Citations in the corpus

• Characterization of the skew-normal distribution (2004, background): “Loperfido (2001), Genton et al. (2001) and Gupta and Huang (2002) focused on probabilistic properties of quadratic skew-normal variates.”
• Skew normal measurement error models (2005, background): “[14] derive the moments of a random vector with multivariate skew normal distribution and their quadratic forms.”
• The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “Additional distributional properties can be found in Loperfido (2001) and Genton et al. (2001).”
• A New Spatial Skew-Normal Random Field Model (2007, background): “( 2001 ), one might decide to derive the moments directly from the mgf given in ( 4 ).”
• Generalized skew-elliptical distributions and their quadratic forms (2005, background): “A further generalization is given by Azzalini and Capitanio (1999): if Z ~ SNp(O, ~, c~), then ZTAZ ,~ X2p when A~tA = A. Genton et al. (2001) compute moments of quadratic forms in skew-normal random vectors.”
• A skewed Kalman filter (2005, unknown): “[7] also computed these moments in the special case = 0) M( ) = m(D̃ + t ̃ + t ; ̃t , ̃ + t + D̃+ t ̃ + t (D̃ + t ) T ) m(0; ̃t , ̃ + t + D̃+ t ̃ + t (D̃ + t ) T ) exp{( ̃t ) + 1 2 ( t ̃ + t )}.”
• On fundamental skew distributions (2005, background): “[15] derive the moments of random vectors with multivariateSNdistributions and their quadratic forms (see also [24]).”
• The multivariate skew-slash distribution (2006, methodology): “Using the same argument as for the multivariate slash distribution, the moments of X ∼ SSLp( , , q, ) follow readily from (7) and the moments of Y ∼ SNp(0, Ip, ), see e.g. Genton et al. (2001).”
• A class of multivariate skew-normal models (2004, background): “For example, the application of skew normal distribution to time series and spatial statistics was discussed by Genton et al. (2001), among others.”
• A SKEW-SYMMETRIC REPRESENTATION OF MULTIVARIATE DISTRIBUTIONS (2002, unknown): “Genton and Loperfido (2002) showed that the distribution of any even function, in particular quadratic forms, in GSE random vectors does not depend on the skewing function π.”
• Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution (2003, methodology): “while, for the expressions of , we use results given by Azzalini & Capitanio (1999) and by Genton et al. (2001). First, we apply (28) to the scalar case.”
• Generalized skew-Cauchy distribution ☆ (2007, background): “Quadratic forms of skew-normal random vectors have been studied by Azzalini (1985), Azzalini and Dalla Valle (1996), Azzalini and Capitanio (1999), Loperfido (2001), Genton et al. (2001), and Gupta and Huang (2002).”