copBasic (version 1.6.0)

isCOP.radsym: Is a Copula Radially Symmetric

Description

Numerically set a logical whether a copula is radially symmetric (Nelson, 2006, p. 37). A copula $\mathbf{C}(u,v)$ is radially symmetric if and only if for any ${u,v} \in [0,1]$ the following hold $$\mathbf{C}(u,v) = u + v - 1 + \mathbf{C}(1-u, 1-v)$$ or $$u + v - 1 + \mathbf{C}(1-u, 1-v) - \mathbf{C}(u,v) \equiv 0\mbox{.}$$

Usage

isCOP.radsym(cop=NULL, para=NULL, delta=0.005, tol=1e-4, ...)

Arguments

cop

A copula function;

para

Vector of parameters, if needed, to pass to the copula;

delta

The increments of ${u,v} \mapsto [0+\Delta\delta, 1-\Delta\delta, \Delta\delta]$;

tol

A tolerance on the check for symmetry, default 1 part in 10,000, which is the test for the $\equiv 0$ (zero equivalence, see source code); and

...

Additional arguments to pass to the copula or derivative of a copula function.

Value

• A logical TRUE or FALSE is returned.

References

Nelson, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

See Also

COP

Examples

isCOP.radsym(cop=P) # TRUE
para <- list(cop1=PLACKETTcop, cop2=M, para1=c(.3), para2=NA, alpha=0.8, beta=0.5)
isCOP.radsym(composite2COP, para=para) # FALSE