Univariate and bivariate truncated von Mises distributions
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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.
KeywordsAngular 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.
- 1.Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Dover Publications, New York (1964)Google Scholar
- 2.Bistrian, D.A., Iakob, M.: One-dimensional truncated von Mises distribution in data modeling. Ann. Fac. Eng. Hunedoara tome VI, fascicule 3 (2008)Google Scholar
- 3.Bowyer, P., N.M.T., Danson, F.M.: SAFARI 2000 Canopy Structural Measurements, Kalahari Transect, Wet Season 2001. Data set (2005)Google Scholar
- 5.Lopez-Cruz, P., Bielza, C., Larrañaga, P.: Directional naive Bayes classifiers. Pattern Anal. Appl., pp. 1–22 (2013)Google Scholar
- 6.Mardia, K., Jupp, P.: Directional Statistics. Wiley Series in Probability and Statistics (2000)Google Scholar