Generate a gridded representation of the bivariate empirical copula (see <code>EMPIRcop</code>, Salvadori et al., 2007, p. 140). This function has the primary intention of supporting 3-D renderings or 2-D images of the copulatic surface, but many empirical copula functions in copBasic rely on the grid of the empirical copula---unlike the functions that support parametric copulas.

EMPIRgrid

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

EMPIRgrid function

Grid of the Bivariate Empirical Copula — EMPIRgrid

<dl>

 <dt>para</dt>
<dd>A vector (single element) of parameters---the U-statistics of the data (see example);</dd>

 <dt>deluv</dt>
<dd>A delta value of the both the \(u\) and \(v\) axes (grid edges) for empirical copula estimation by the <code>EMPIRcop</code> function;</dd>

 <dt>verbose</dt>
<dd>A logical controlling whether the progress during grid building is to be shown; and</dd>

 <dt>...</dt>
<dd>Additional arguments to pass to <code>EMPIRcop</code>.</dd>

</dl>

EMPIRgrid: Grid of the Bivariate Empirical Copula

Description

Usage

Arguments

Value

References

See Also