EXPERIMENTAL---Perform a simulation on a bivariate empirical copula to produce the random variates $U$ and $V$ and return an R <code>data.frame</code> of them. The method is more broadly known as conditional simulation method. This function is an empirical parallel to <code>simCOP</code> that is used for parametric copulas. If circumstances require conditional simulation of $V{\mid}U$, then function <code>EMPIRsimv</code>, which produces a vector of $V$ from a fixed $u$, should be used.
For the usual situation in which an individual $u$ during the simulation loops is not a value aligned on the grid, then the bounding conditional quantile functions are solved for each of the $n$ simulations and the following interpolation is made by
$$v = \frac{v_1/w_1 + v_2/w_2}{1/w_1 + 1/w_2}\mbox{,}$$
which states that that the weighted mean is computed. The values $v_1$ and $v_2$ are ordinates of the conditional quantile function for the respective grid lines to the left and right of the $u$ value. The values $w_1$ $=$ $u - u^\mathrm{left}_\mathrm{grid}$ and $w_2$ $=$ $u^\mathrm{right}_\mathrm{grid} - u$.

EMPIRsim

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

EMPIRsim function

Simulate a Bivariate Empirical Copula — EMPIRsim

<dl>

 <dt>n</dt>
<dd>A sample size, default is 100;</dd>

 <dt>empgrid</dt>
<dd>Gridded empirical copula from <code>EMPIRgrid</code>;</dd>

 <dt>kumaraswamy</dt>
<dd>A logical to trigger Kumaraswamy distribution smoothing of the conditional quantile function that is passed to <code>EMPIRgridderinv</code>. The Kumaraswamy distribution is a distribution having support $[0,1]$ with an explicit quantile function and takes the place of a Beta distribution (see lmomco function <code>quakur()</code> for more details);</dd>

 <dt>na.rm</dt>
<dd>A logical to toggle the removal of <code>NA</code> entries on the returned <code>data.frame</code>;</dd>

 <dt>keept</dt>
<dd>Keep the $t$ uniform random variable for the simulation as the last column in the returned <code>data.frame</code>;</dd>

 <dt>graphics</dt>
<dd>A logical that will disable graphics by setting <code>ploton</code> and <code>points</code> to <code>FALSE</code> and overriding whatever their settings were;</dd>

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

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

 <dt>snv</dt>
<dd>A logical to convert the $\{u,v\}$ to standard normal scores (variates) both for the optional graphics and the returned <code>data.frame</code>. Joe (2014) advocates extensively for use of normal scores, which is in contrast to Nelsen (2006) who does not;</dd>

 <dt>infsnv.rm</dt>
<dd>A logical that will quietly strip out any occurrences of $u = \{0,1\}$ or $v = \{0,1\}$ from the simulations because these are infinity in magnitude when converted to standard normal variates is to occur. Thus, this logical only impacts logic flow when <code>snv</code> is <code>TRUE</code>. The <code>infsnv.rm</code> is mutually exclusive from <code>trapinfsnv</code>;</dd>

 <dt>trapinfsnv</dt>
<dd>If <code>TRUE</code> and presumably small, the numerical value of this argument ($\eta$) is used to replace $u = \{0,1\}$ and $v = \{0,1\}$ with $u(0) = v(0) = \eta$ or $u(1) = v(1) = 1 - \eta$ as appropriate when conversion to standard normal variates is to occur. The setting of <code>trapinfsnv</code> only is used if <code>snv</code> is <code>TRUE</code> and <code>infsnv.rm</code> is <code>FALSE</code>; and</dd>

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

</dl>

EMPIRsim: Simulate a Bivariate Empirical Copula

Description

Usage

Arguments

Value

See Also