cyl_rect_combine-class | R Documentation |
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.
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.
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 are created by
cyl_rect_combine()
.
Class 'cyl_rect_combine
' extends class 'Copula
'.
Durante2009cylcop
\insertRefHodelapplcylcop
\insertRefHodelmethodcylcop
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