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

  • Arjun K. Gupta Bowling Green State University
  • Tõnu Kollo University of Tartu
  • Anne Selart University of Tartu
Keywords: cumulants, linear form, moments, moment generating function, skew normal distribution


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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Author Biographies

Arjun K. Gupta, Bowling Green State University

Department of Mathematics and Statistics

Tõnu Kollo, University of Tartu

Institute of Mathematical Statistics

Anne Selart, University of Tartu

Institute of Mathematical Statistics