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. 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 is a generalization of the non-truncated marginal distribution. From the viewpoint of applications, we test the distribution with data regarding leaf inclination angles. This research aims to assert this probability distribution as a potential option for modeling or simulating any kind of phenomena where circular distributions are applicable.