根据参考论文：https://www.aimspress.com/article/10.3934/mbe.2017038/fulltext.html
an explicit formula for the three dimensional variance
In Section 4 we apply this method to compute the first and second moment in three dimensions (in three dimensions the von Mises distribution is generally known as the Fisher or von Mises-Fisher distribution [20,1]1). To our knowledge, an explicit formula for the three dimensional variance is not known in the literature and here we provide such a formula. Moreover, this method generalises to higher space dimensions and other circular/spherical distributions.