EXPERIMENTAL---This function converts the L-comoments of a bivariate sample to the four parameters of a composition of two one-parameter copulas. Critical inputs are of course the first three dimensionless L-comoments: L-correlation, L-coskew, and L-cokurtosis. The most complex input is the solutionenvir, which is an environment containing arbitrarily long, but individual tables, of L-comoment and parameter pairings. These pairings could be computed from the examples in simcompositeCOP.
The individual tables are prescanned for potentially acceptable solutions and the absolute additive error of both L-comoments for a given order is controlled by the tNeps arguments. The default values seem acceptable. The purpose of the prescanning is to reduce the computation space from perhaps millions of solutions to a few orders of magnitude. The computation of the solution error can be further controlled by \(X\) or \(u\) with respect to \(Y\) or \(v\) using the comptNerrXY arguments, but experiments thus far indicate that the defaults are likely the most desired. A solution “matching” the L-correlation is always sought; thus there is no uset2err argument. The arguments uset3err and uset4err provide some level of granular control on addition error minimization; the defaults seek to “match” L-coskew and ignore L-cokurtosis. The setreturn controls which rank of computed solution is returned; users might want to manually inspect a few of the most favorable solutions, which can be done by the setreturn or inspection of the returned object from the lcomoms2.cop2parameter function. The examples are detailed and self-contained to the copBasic package; curious users are asked to test these.
lcomoms2.ABcop2parameter(solutionenvir=NULL,
T2.12=NULL, T2.21=NULL,
T3.12=NULL, T3.21=NULL,
T4.12=NULL, T4.21=NULL,
t2eps=0.1, t3eps=0.1, t4eps=0.1,
compt2erruv=TRUE, compt2errvu=TRUE,
compt3erruv=TRUE, compt3errvu=TRUE,
compt4erruv=TRUE, compt4errvu=TRUE,
uset3err=TRUE, uset4err=FALSE,
setreturn=1, maxtokeep=1e5)An R
data.frame is returned.
The environment containing solutions;
L-correlation \(\tau_2^{[12]}\);
L-correlation \(\tau_2^{[21]}\);
L-coskew \(\tau_3^{[12]}\);
L-coskew \(\tau_3^{[21]}\);
L-cokurtosis \(\tau_4^{[12]}\);
L-cokurtosis \(\tau_4^{[21]}\);
An error term in which to pick a potential solution as close enough on preliminary processing for \(\tau_2^{[1 \leftrightarrow 2]}\);
An error term in which to pick a potential solution as close enough on preliminary processing for \(\tau_3^{[1 \leftrightarrow 2]}\);
An error term in which to pick a potential solution as close enough on preliminary processing for \(\tau_4^{[1 \leftrightarrow 2]}\);
Compute an L-correlation error using the 1 with respect to 2 (or \(u\) wrt \(v\));
Compute an L-correlation error using the 2 with respect to 1 (or \(v\) wrt \(u\));
Compute an L-coskew error using the 1 with respect to 2 (or \(u\) wrt \(v\));
Compute an L-coskew error using the 2 with respect to 1 (or \(v\) wrt \(u\));
Compute an L-cokurtosis error using the 1 with respect to 2 (or \(u\) wrt \(v\));
Compute an L-cokurtosis error using the 2 with respect to 1 (or \(v\) wrt \(u\));
Use the L-coskew error in the determination of the solution. The L-correlation error is always used;
Use the L-cokurtosis error in the determination of the solution. The L-correlation error is always used;
Set (index) number of the solution to return. The default of 1 returns the preferred solutions based on the controls for the minimization; and
The value presets the number of rows in the solution matrix. This matrix is filled with potential solutions as the various subfiles of the solutionenvir are scanned. The matrix is trimmed of NAs and error trapping is in place for too small values of maxtokeep. The default value appears appropriate for the feeding of massively large simulated parameter spaces.
W.H. Asquith
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.
Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in Nature---An approach using copulas: Springer, 289 p.
simCOP, simcompositeCOP, composite2COP