Univariate and bivariate truncated von Mises distributions

Abstract

In this article we study the univariate and bivariate truncated von Mises distribution, as a generalization of the von Mises distribution (Jupp and Mardia (1989)), (Mardia and Jupp (2000)). This implies the addition of two or four new truncation parameters in the univariate and, bivariate cases, respectively. The results include the definition, properties of the distribution and maximum likelihood estimators for the univariate and bivariate cases. Additionally, the analysis of the bivariate case shows how the conditional distribution is a truncated von Mises distribution, whereas the marginal distribution that generalizes the distribution introduced in Singh (2002). From the viewpoint of applications, we test the distribution with simulated data, as well as with data regarding leaf inclination angles (Bowyer and Danson. (2005)) and dihedral angles in protein chains (Murzin AG (1995)).This research aims to assert this probability distribution as a potential option for modelling or simulating any kind of phenomena where circular distributions are applicable.

Review on Outliers Identification Methods for Univariate Circular Biological Data

“…Also, [28] used von Mises distribution to propose a new definition of truncated probability distribution for univariate and bivariate circular data which is applied to protein chains for angular values. Besides, [15] used von Mises distribution for adjusting and detecting outliers of the sea star directions using robust circular distance.…”