Abstract
This paper provides a formal asymptotic expansion of a sampling distribution of Generalized non-central F-statistic which is introduced by Fang and Zhang (1990, pp.86-88) and Mathai et al. (1995, p.99) under elliptical populations. In many cases, asymptotic expansions of distribution of non-central F-type statistic would be expressed by a weighted sum of non-central χ^2-distribution. For the generalized non-central F-statistic, however, the asymptotic expansion can be written in terms of non-central F-distribution. In the sequel, to evaluate the accuracy of the asymptotic expansion, we carry out some numerical experiments under typical elliptical distributions, namely, the normal distribution, the t-distribution and "ε-contaminated" normal distribution.
