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Statistical modeling of directional data using a robust hierarchical von mises distribution model: perspectives for wind energy

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Abstract

For describing wind direction, a variety of statistical distributions has been suggested that provides information about the wind regime at a particular location and aids the development of efficient wind energy generation. In this paper a systematic approach for data classification putting a special emphasis on the von Mises mixtures is presented. A von Mises mixture model is broad enough to cover, on one hand, symmetry and asymmetry, on the other hand, unimodality and multimodality of circular data. We developed an improved mathematical model of the classical von Mises mixture method, rests on number of principles which gives its internal coherence and originality. In principle, our hierarchical model of von Mises distributions is flexible to precisely modeled complex directional data sets. We define a new specific expectation–maximization (S-EM) algorithm for estimating the parameters of the model. The simulation showed that satisfactory fit of complex directional data could be obtained (error generally < 1%). Furthermore, the Bayesian Information Criterion is used to judge the goodness of fit and the suitability for this model versus common distributions found in the literature. The findings prove that our hierarchical model of von Mises distributions is relevant for modeling the complex directional data with several modes and/or prevailing data directions.

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Authors and Affiliations

  1. LRIT URAC 29, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

    Said Benlakhdar & Mohammed Rziza

  2. RIITM, ENSIAS, Mohammed V University in Rabat, Rabat, Morocco

    Rachid Oulad Haj Thami

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  1. Said Benlakhdar
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  2. Mohammed Rziza
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  3. Rachid Oulad Haj Thami
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Correspondence to Said Benlakhdar.

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Benlakhdar, S., Rziza, M. & Thami, R.O.H. Statistical modeling of directional data using a robust hierarchical von mises distribution model: perspectives for wind energy. Comput Stat 37, 1599–1619 (2022). https://doi.org/10.1007/s00180-021-01173-5

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