Nonsingular Information Matrix and the Von Mises Fisher Distribution

In this article, the asymptotic distribution of the deviance statistic for some hypothesis tests concerning the parameters of the von Mises Fisher distribution is discussed. The focus is on the likelihood of the distribution which is a new exposition in the literature of the direc-tional distributions. To find the distribution of the deviance statistic, we use Chernoff’ s idea about the distance from the cone built upon the null and alternative hypotheses.