Progress in Artificial Intelligence

, Volume 6, Issue 2, pp 171–180 | Cite as

Univariate and bivariate truncated von Mises distributions

  • Pablo Fernandez-Gonzalez
  • Concha Bielza
  • Pedro Larrañaga
Regular Paper


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.


Angular probability distributions Directional statistics von Mises distribution Truncated probability distributions 



This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through the Cajal Blue Brain (C080020-09; the Spanish partner of the Blue Brain initiative from EPFL) and TIN2013-41592-P projects, by the Regional Government of Madrid through the S2013/ICE-2845-CASI-CAM-CM project.

Supplementary material

13748_2016_109_MOESM1_ESM.pdf (441 kb)
Supplementary material 1 (pdf 440 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Pablo Fernandez-Gonzalez
    • 1
  • Concha Bielza
    • 1
  • Pedro Larrañaga
    • 1
  1. 1.Department of Artificial IntelligenceUniversidad Politécnica de MadridMadridSpain

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