A Mobius transformation-induced distribution on the torus

• 成果类型: Article
• 署名作者: Kato, Shogo; Pewsey, Arthur
• 署名单位: Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Universidad de Extremadura
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv003
• 发表日期: 2015
• 页码: 359370
• 关键词: correlation-coefficient; models; statistics; tests

摘要

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 Mobius 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.