For a class of multivariate skew normal distributions, the noncentral skew chi-square distribution is studied. The necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi-square distributed random variables are obtained. Several examples...

This paper examines asymptotic distributions of the canonical correlations between and with q<=p, based on a sample of size of N=n+1. The asymptotic distributions of the canonical correlations have been studied extensively when the dimensions q and p are fixed and the sample size N tends toward infinity. However, these approximations worsen when q or p is large in comparison to N. To overcome this weakness, this paper first derives asymptotic distributions of the canonical correlations under a high-dimensional framework such that q is fixed, m=n-p-->[infinity] and c=p/n--c0[set membership, variant][0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher's z-transformation is proposed. Then, the asymptotic...</=p,>

While the noncentral Wishart distribution is generally introduced as the distribution of the random symmetric matrix where Y1,...,Yn are independent Gaussian rows in with the same covariance, the present paper starts from a slightly more general definition, following the extension of the...