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A Möbius transformation-induced distribution on the torus. (English) Zbl 1452.62188
Summary: We propose a five-parameter bivariate wrapped Cauchy distribution as a unimodal model for toroidal data. It is highly tractable, displays numerous desirable properties, including marginal and conditional distributions that are all wrapped Cauchy, and arises as an appealing submodel of a six-parameter distribution obtained by applying Möbius transformation to a pre-existing bivariate circular model. Method of moments and maximum likelihood estimation of its parameters are fast, and tests for independence and goodness-of-fit are available. An analysis involving dihedral angles of the proteinogenic amino acid Tyrosine illustrates the distribution’s application. A Markov process for circular data is also explored.

MSC:
62E15 Exact distribution theory in statistics
62F10 Point estimation
62R40 Topological data analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
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