Compute and plot level curves or level sets of a copula for $U$ with respect to $V$ (Nelsen, 2006, pp. 12--13). The level curves at a levels $t \mapsto [0+\Delta t, 1-\Delta t, \Delta t]$ are defined for $V \mapsto [0+\Delta v, 1-\Delta v, \Delta v]$ by
$$t = \mathbf{C}(u, v=V)\mbox{,}$$
and solving for $u$. Plotting is provided by this function because level curves are such an important visual attribute of a copula and highly useful for pedagogic purposes. The above equation is implemented by the inverse of a copula using <code>COPinv2</code>.

level.curvesCOP2

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.curvesCOP2 function

Compute and Plot Level Curves of a Copula U with respect to V — level.curvesCOP2

<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>ploton</dt>
<dd>A logical to toggle on the plot;</dd>

 <dt>lines</dt>
<dd>A logical to toggle calls to the <code><a href='https://rdrr.io/r/graphics/lines.html'>lines()</a></code> function in R to draw the lines;</dd>

 <dt>plotMW</dt>
<dd>A logical to toggle to use <code><a href='https://rdrr.io/r/graphics/abline.html'>abline()</a></code> function in R to plot cross lines for the $\mathbf{M}$ (<code>M</code>) and $\mathbf{W}$ (<code>W</code>) copulas;</dd>

 <dt>ramp</dt>
<dd>A logical to toggle whether the level curves are ramped in thickness according to the probability of the line. The argument can be used with a <code>lwd</code> setting through the <code>...</code> and can either be a constant, which will override the built-in ramp, or <code>lwd</code> can be defined as a function to replace the built-in ramp in terms of the probability;</dd>

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

 <dt>delt</dt>
<dd>The increment of $\Delta t$ for the level curves to plot, defaults to 10-percent intervals;</dd>

 <dt>getlevel</dt>
<dd>If defined and level exists upon stepping through using <code>delt</code>, then the level curve at the <code>getlevel</code> is returned in an R <code>list</code> data structure;</dd>

 <dt>silent</dt>
<dd>The argument of the same name given over to <code><a href='https://rdrr.io/r/base/try.html'>try()</a></code> wrapping the <code><a href='https://rdrr.io/r/base/try.html'>try()</a></code> operation on forming sequences of $t$ for the curves (see sources); 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.curvesCOP2: Compute and Plot Level Curves of a Copula U with respect to V

Description

Usage

Arguments

Value

References

See Also