On the joint distribution of a linear and a quadratic form in skew normal variables | Zendy

Arjun K. Gupta | Zendy; Tõnu Kollo | Zendy; Anne Selart | Zendy

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On the joint distribution of a linear and a quadratic form in skew normal variables

Author(s) -

Arjun K. Gupta,

Tõnu Kollo,

Anne Selart

Publication year - 2007

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2007.11.04

Subject(s) - cumulant , skew , skew normal distribution , multivariate normal distribution , mathematics , multivariate statistics , independence (probability theory) , quadratic equation , moment (physics) , joint probability distribution , quadratic form (statistics) , joint (building) , distribution (mathematics) , combinatorics , mathematical analysis , statistics , computer science , physics , geometry , engineering , architectural engineering , telecommunications , classical mechanics

Let z be distributed as multivariate skew normal vector. We derive the joint moment generating function (m.g.f.) of a linear form and a quadratic form in z, and the conditions for their independence. The first two multivariate cumulants of the two forms are derived and applied in special cases. Finally a simulation example is presented.

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