Properties of Statistical Distribution for Dihedral Angles

Bivariate Von Mises distribution، which behaves relatively similar to bivariate normal distributions، have been proposed for representing the simultaneously probabilistic variability of these angles. One of the remarkable properties of this distribution is having the univariate Von Mises as the conditional density. However، the marginal density takes various structures depend on its involved parameters and، in general، has no closed form. This issue encounters the statistical inference with particular problems. In this paper، this distribution and its properties is studied، then the procedure to sample via the acceptance-rejection algorithm is described. The problems encountered in choosing a proper candidate distribution، arising from the cyclic feature of both angles، is investigated and the properties of its conditional density is utilized to overcome this obstacle.