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.ABKGcop2parameter function. The examples are detailed and self-contained to the copBasic package; curious users are asked to test these.
lcomoms2.ABKGcop2parameter(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.
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, composite3COP