Compute a level curve or level set of a copula for $V$ with respect to $U$ (Nelsen, 2006, pp. 12--13). The level curve at level $t$ is defined for $U \mapsto [0+\Delta u, 1-\Delta u, \Delta u]$ by
$$t \mapsto \mathbf{C}(u{=}U, v)\mbox{,}$$
and solving for $v$. The function is largely a dispatcher to features implemented in <code>level.curvesCOP</code>.

level.setCOP

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

level.setCOP function

Compute a Level Set of a Copula V with respect to U — level.setCOP

<dl>

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

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

 <dt>getlevel</dt>
<dd>The level set for $t$;</dd>

 <dt>delu</dt>
<dd>The increment for $\Delta u$. The default is 1 part in 1,000, which should often in practice provide enough smoothness for many copulas;</dd>

 <dt>lines</dt>
<dd>A logical that matches the argument of the same name in <code>level.curvesCOP</code>; and</dd>

 <dt>...</dt>
<dd>Additional arguments to pass to the <code><a href='https://rdrr.io/r/graphics/lines.html'>lines()</a></code> function in R.</dd>

</dl>

level.setCOP: Compute a Level Set of a Copula V with respect to U

Description

Usage

Arguments

Value

References

See Also