Quadratic forms of refined skew normal models based on stochastic representation
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Weizhong Tian
und
Tonghui Wang
Abstract
Wang, Li and Gupta [17] first introduced the skew chi-square distribution based on the multivariate skew normal distribution provided by Azzalini [2], and Ye, Wang and Gupta [18] extended this results into the skew Wishart distribution. Motivated by these results, we first study a new type of multivariate skew normal distribution introduced by Gupta and Chen [12], the moment generating function, independence and quadratic form are discussed, and also a new type of skew chi-square distribution was introduced. Later on, we defined a new type of skew Wishart distribution based on the matrix skew normal models introduced by Ning [15]. In the end, we will study the probabilistic representation of multivariate skew elliptical models.
Acknowledgements
We gratefully acknowledge referees for their valuable comments and suggestions which greatly improve this paper.
References
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Stochastic flows associated with Stratonovich curve-line integrals
- Quadratic forms of refined skew normal models based on stochastic representation
- On the 70th years of Vyacheslav Girko and over a hundred laws of his M.A.G.I.C.-theory
- Time varying axially symmetric vector random fields on the sphere
- Stability of fractional neutral stochastic partial integro-differential equations
Artikel in diesem Heft
- Frontmatter
- Stochastic flows associated with Stratonovich curve-line integrals
- Quadratic forms of refined skew normal models based on stochastic representation
- On the 70th years of Vyacheslav Girko and over a hundred laws of his M.A.G.I.C.-theory
- Time varying axially symmetric vector random fields on the sphere
- Stability of fractional neutral stochastic partial integro-differential equations
