Dependent models for observations which include angular ones |
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Authors: | Shogo Kato Kunio Shimizu |
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Institution: | 1. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan;2. Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan |
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Abstract: | This paper discusses some stochastic models for dependence of observations which include angular ones. First, we provide a theorem which constructs four-dimensional distributions with specified bivariate marginals on certain manifolds such as two tori, cylinders or discs. Some properties of the submodel of the proposed models are investigated. The theorem is also applicable to the construction of a related Markov process, models for incomplete observations, and distributions with specified marginals on the disc. Second, two maximum entropy distributions on the cylinder are discussed. The circular marginal of each model is distributed as the generalized von Mises distribution which represents a symmetric or asymmetric, unimodal or bimodal shape. The proposed cylindrical model is applied to two data sets. |
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Keywords: | Copula Directional statistics Markov process Maximum entropy von Mises distribution |
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