cyl_rect_combine-class {cylcop}

An S4 Class of Circular-Linear Copulas Generated from a Rectangular Patchwork

Description

This class contains bivariate circular-linear copulas generated from linear-linear bivariate 'Copula' objects of the package 'copula' or circular-linear copulas of class 'cyl_copula'. 2 non-overlapping rectangles are laid over the unit square, both have width 1 in v-direction. In the area covered by the first rectangle, the copula is derived from a linear-linear bivariate 'Copula' object. Rectangle 2 contains the same copula as rectangle 1, but 90 degrees rotated. In the area not covered by the rectangles, the "background", the copula is derived from a circular-linear 'cyl_copula' object. The copula regions are combined in a way that the overall result on the entire unit square is also a copula.

Details

With appropriate choices of the rectangles this results in copulas that are periodic in u-direction (and not in v-direction) and therefore are circular-linear. When the 2 rectangles are mirror images with respect to u=0.5, the resulting overall copula is symmetric with respect to u=0.5, i.e. there is symmetry between positive and negative angles.

Note that as "background copula", we can also chose a linear-linear copula, the overall result will then, however, not be a symmetric circular linear copula.

Slots

name

character string holding the name of the copula.

parameters

numeric vector holding the parameter values.

param.names

character vector the parameter names.

param.lowbnd

numeric vector holding the lower bounds of the parameters.

param.upbnd

numeric vector holding the upper bounds of the parameters.

sym.cop

'Copula' object of the package 'copula' or 'cyl_vonmises' object. The copula in the rectangles.

background.cop

'cyl_vonmises' or 'Copula' object of the package 'copula', the copula where no rectangles overlay the unit square. If this copula is not symmetric, the overall cyl_rect_combine-copula will also not be symmetric.

flip_up

logical value indicating whether the copula (sym.cop) is rotated 90 degrees in the upper or lower rectangle.

sym_rect

logical value indicating whether the upper rectangle was forced to be a mirror image of the lower one with respect to u=0.5 at the construction of the object.

Objects from the Class

Objects are created by cyl_rect_combine().

Extends

Class 'cyl_rect_combine' extends class 'Copula'.

References

Durante F, Saminger-Platz S, Sarkoci P (2009). “Rectangular patchwork for bivariate copulas and tail dependence.” Communications in Statistics - Theory and Methods, 38(15), 2515–2527. ISSN 03610926, doi:10.1080/03610920802571203.

Hodel FH, Fieberg JR (2022). “Circular-Linear Copulae for Animal Movement Data.” Methods in Ecology and Evolution. doi:10.1111/2041-210X.13821.

Hodel FH, Fieberg JR (2021). “Cylcop: An R Package for Circular-Linear Copulae with Angular Symmetry.” bioRxiv. doi:10.1101/2021.07.14.452253, https://www.biorxiv.org/content/10.1101/2021.07.14.452253v3/.