isCOP.permsym

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.

copula (properties)

copula (symmetry)

copula (characteristics)

Extensive functions for bivariate copula (bicopula) computations and related operations
for bicopula theory. The lower, upper, product, and select other bicopula are implemented along
with operations including the diagonal, survival copula, dual of a copula, co-copula, and
numerical bicopula density. Level sets, horizontal and vertical sections are supported. Numerical
derivatives and inverses of a bicopula are provided through which simulation is implemented.
Bicopula composition, convex combination, asymmetry extension, and products also are provided.
Support extends to the Kendall Function as well as the Lmoments thereof. Kendall Tau,
Spearman Rho and Footrule, Gini Gamma, Blomqvist Beta, Hoeffding Phi, Schweizer-
Wolff Sigma, tail dependency, tail order, skewness, and bivariate Lmoments are implemented, and
positive/negative quadrant dependency, left (right) increasing (decreasing) are available.
Other features include Kullback-Leibler Divergence, Vuong Procedure, spectral measure, and
Lcomoments for inference, maximum likelihood, and AIC, BIC, and RMSE for goodness-of-fit.

William Asquith

copBasic

General Bivariate Copula Theory and Many Utility Functions

isCOP.permsym function

<dl> <dt>cop</dt>
<dd>A copula function;</dd> <dt>para</dt>
<dd>Vector of parameters, if needed, to pass to the copula;</dd> <dt>delta</dt>
<dd>The increment of $\{u,v\} \mapsto [0+\Delta\delta, 1-\Delta\delta, \Delta\delta]$;</dd> <dt>tol</dt>
<dd>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</dd> <dt>...</dt>
<dd>Additional arguments to pass to the copula.</dd></dl>

Arguments

Author

Is a Copula Permutation Symmetric — isCOP.permsym

<dl>

 <dt>cop</dt>
<dd>A copula function;</dd>

 <dt>para</dt>
<dd>Vector of parameters, if needed, to pass to the copula;</dd>

 <dt>delta</dt>
<dd>The increment of $\{u,v\} \mapsto [0+\Delta\delta, 1-\Delta\delta, \Delta\delta]$;</dd>

 <dt>tol</dt>
<dd>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</dd>

 <dt>...</dt>
<dd>Additional arguments to pass to the copula.</dd>

</dl>

isCOP.permsym: Is a Copula Permutation Symmetric

Description

Usage

Value

Arguments

Author

References

See Also