Open AccessOn 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./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.