EXPERIMENTAL---Perform a simulation on a bivariate empirical copula to extract the random variates \(V\) from a given and fixed value for \(u=\) constant. The purpose of this function is to return a simple vector of the \(V\) simulations. This behavior is similar to simCOPmicro but differs from the general 2-D simulation implemented in the other functions: EMPIRsim and simCOP---these two functions generate R data.frames of simulated random variates \(U\) and \(V\) and optional graphics as well.
For the usual situation in which \(u\) 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 \(w_2\) \(=\) \(u^\mathrm{right}_\mathrm{grid} - u\).
EMPIRsimv(u, n=1, empgrid=NULL, kumaraswamy=FALSE, ...)A vector of simulated \(V\) values is returned.
The fixed probability \(u\) on which to perform conditional simulation for a sample of size \(n\);
A sample size, default is 1;
Gridded empirical copula from EMPIRgrid;
A logical to trigger Kumaraswamy distribution smoothing of the conditional quantile function that is passed to EMPIRgridderinv. 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 quakur() for more details); and
Additional arguments to pass.
W.H. Asquith
EMPIRgrid, EMPIRsim