A study of generalized skew-normal distribution

作者：Huang Wen Jang; Su Nan Cheng^*; Gupta Arjun K

来源：Statistics, 2013, 47(5): 942-953.

DOI：10.1080/02331888.2012.697164

• elliptical distribution
• independence
• moment-generating function
• multivariate skew-normal distribution
• quadratic form

Following the paper by Genton and Loperfido [Generalized skew-elliptical distributions and their quadratic forms, Ann. Inst. Statist. Math. 57 (2005), pp. 389-401], we say that Z has a generalized skew-normal distribution, if its probability density p.d.f.) is given by f(z)=2 phi(p)(z; , ) (z-), z(p), where phi(p)(; , ) is the p-dimensional normal p.d.f. with location vector and scale matrix , (p), %26gt;0, and is a skewing function from (p) to , that is 0 (z)1 and (-z)=1- (z), ? z(p). First the distribution of linear transformations of Z are studied, and some moments of Z and its quadratic forms are derived. Next we obtain the joint moment-generating functions (m.g.f.%26apos;s) of linear and quadratic forms of Z and then investigate conditions for their independence. Finally explicit forms for the above distributions, m.g.f.%26apos;s and moments are derived when (z)= (z), where (p) and is the normal, Laplace, logistic or uniform distribution function.

• 出版日期2013-10-1