Title: Circulas obtained through a Fourier series based approach
Authors: Shogo Kato - Institute of Statistical Mathematics (Japan) [presenting]
Arthur Pewsey - University of Extremadura (Spain)
Chris Jones - The Open University (United Kingdom)
Abstract: Circular data are a set of observations which can be expressed as angles $[-\pi,\pi)$. Bivariate circular data, comprised of pairs of circular observations $[-\pi,\pi)^2$, arise in numerous contexts. A general method is proposed to obtain copulas for bivariate circular data which are called circulas. This is achieved first by representing probability density functions of bivariate circular distributions in terms of Fourier series. With this representation, some conditions on the Fourier coefficients which produce a general family of circulas are presented. Then, as special cases of the general family, some classes of circulas arising from different patterns of non-zero Fourier coefficients are considered. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. All the special cases of the considered circulas have simple closed-form expressions for their densities and display different dependence structures between variables.