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Univariate and bivariate truncated von Mises distributions

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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.

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References

  1. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Dover Publications, New York (1964)

  2. Bistrian, D.A., Iakob, M.: One-dimensional truncated von Mises distribution in data modeling. Ann. Fac. Eng. Hunedoara tome VI, fascicule 3 (2008)

  3. Bowyer, P., N.M.T., Danson, F.M.: SAFARI 2000 Canopy Structural Measurements, Kalahari Transect, Wet Season 2001. Data set (2005)

  4. Jupp, P.E., Mardia, K.V.: A unified view of the theory of directional statistics, 1975–1988. Int. Stat. Rev. 57(3), 261–294 (1989)

    Article  MATH  Google Scholar 

  5. Lopez-Cruz, P., Bielza, C., Larrañaga, P.: Directional naive Bayes classifiers. Pattern Anal. Appl., pp. 1–22 (2013)

  6. Mardia, K., Jupp, P.: Directional Statistics. Wiley Series in Probability and Statistics (2000)

  7. Mardia, K.V., Hughes, G., Taylor, C.C., Singh, H.: A multivariate von Mises distribution with applications to bioinformatics. Can. J. Stat. 36, 99–109 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mardia, K.V., Voss, J.: Some fundamental properties of a multivariate von Mises distribution. Commun. Stat. Theory Methods 43(6), 1132–1144 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Singh, H.: Probabilistic model for two dependent circular variables. Biometrika 89(3), 719–723 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

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.

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  1. Department of Artificial Intelligence, Universidad Politécnica de Madrid, Madrid, Spain

    Pablo Fernandez-Gonzalez, Concha Bielza & Pedro Larrañaga

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  1. Pablo Fernandez-Gonzalez
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  2. Concha Bielza
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  3. Pedro Larrañaga
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Correspondence to Pablo Fernandez-Gonzalez.

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Fernandez-Gonzalez, P., Bielza, C. & Larrañaga, P. Univariate and bivariate truncated von Mises distributions. Prog Artif Intell 6, 171–180 (2017). https://doi.org/10.1007/s13748-016-0109-x

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  • DOI: https://doi.org/10.1007/s13748-016-0109-x

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