2015/03/19 by Shogo Kato, Arthur Pewsey · 6 citations
Computer Science · Mathematics · Environmental Science · #Bayesian Methods and Mixture Models #Morphological variations and asymmetry #Soil Geostatistics and Mapping
paper · doi:10.1093/biomet/asv003
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.