isCOP.permsym {copBasic}

Is a Copula Permutation Symmetric

Description

Numerically set a logical whether a copula is symmetric (Nelsen, 2006, p. 38), or has exchangable variables, or is permutation symmetric (Joe, 2014, p. 66). A copula \mathbf{C}(u,v) is permutation symmetric if and only if for any \{u,v\} \in [0,1] the following holds

\mathbf{C}(u,v) = \mathbf{C}(v, u)\mbox{.}

The computation is (can be) CPU intensive.

Usage

isCOP.permsym(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 increment 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.

Value

A logical TRUE or FALSE is returned.

Author(s)

W.H. Asquith

References

Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.

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

See Also

LzCOPpermsym, isCOP.radsym

Examples

## Not run: 
isCOP.permsym(cop=GHcop, para=1.3) # TRUE
## End(Not run)