Title: A Cauchy-type model for cylindrical data
Authors: Shogo Kato - Institute of Statistical Mathematics (Japan) [presenting]
Arthur Pewsey - University of Extremadura (Spain)
Abstract: Cylindrical data consist of bivariate observations on a linear variable and circular variable pairing and arise in numerous scientific contexts. A family of five-parameter distributions for cylindrical data is proposed. Its density can be expressed in a simple closed form involving no integrals, infinite sums or special functions. Moreover, the proposed model is unimodal, its five parameters have clear interpretations, and all of its marginal and conditional distributions are either Cauchy or wrapped Cauchy. Related regression models follow from an alternative complex representation of the density, and their regression curves can be expressed using fractional linear transformations. When they exist, the method of moments estimators of the parameters of the proposed cylindrical distribution has closed-form expressions. The Fisher information matrix and the asymptotic covariance matrix for the maximum likelihood estimator have simple closed forms that involve no integrals.