Package: copBasic
Title: Basic Copula Functions
Version: 1.4
Date: 2008-10-30
Author: William H. Asquith
Description: This package implements basic functions for copula
computations and is used by several other packages by the
author. This particular package provides the lower (W), upper
(M), and product (P) copulas as well as the
product-summation-product copula (PSP). Wrapper functions for
the copula (COP), survival copula (surCOP), dual of a copula
(duCOP), and co-copula (coCOP) are provided. The package has
(level.curvesCOP) for drawing level curves of a given copula,
and this function uses the inverse of a copula (COPinv and a
COPinv2 is provided for completeness). The numerical derivative
for the derivative of a copula is provided by (derCOP and
derCOP2) and the inversion of these functions are by (derCOPinv
and derCOPinv2). The diagonal sections of a copula are
supported by (diagCOP), and sections and derivatives of
sections are supported by (sectionCOP). The inverses of copula
derivatives are important for random variate generation. Random
variate generation for a copula using the conditional
distribution method and the deriviative of a copula is provided
by (simCOP and the reduced capability simCOPmicro). For
slightly broader application for purposes of education and
experimentation with copulas, this package also supports the
Plackett copula (PLACKETTcop) because of the general
applicability of this copula. The Plackett copula is
comprehensive, which means that it can attain complete negative
association, independence, and positive association. Plackett
parameter estimation is straightforward with (PLACKETTpar). A
Plackett-specific, random-variate algorithm is by
(PLACKETTsim). Composition of two copulas is provided by
(composite2COP), and composition of one copula is provided by
function (composite1COP).  Composite copula random variates are
generated by (simcompositeCOP). These compositions generally
yield asymmetric copulas. A data set is provided that contains
darts thrown at the L-comoment space of a Plackett-Plackett
composited compula; these data might be used for experimental
copula estimation by the method of L-comoments. The package
also provides a full suite of functions to numerically compute
measures of association through concordance for a given copula
such as Kendall's Tau (tauCOP), Spearman's Rho (rhoCOP), Gini's
Gamma (giniCOP), and Blomqvist's Beta (blomCOP). The Schweizer
and Wolff's Sigma (wolfCOP) is implemented as a measure of
dependency as opposed the the concordance measures just listed.
Upper and lower tail dependence is computed by numerical limit
convergence by (taildepCOP). A numerical computation of the
logical whether a copula is left-tail decreasing or right-tail
increasing is provided by (isCOP.LTD and isCOP.RTI). The
package supports quantile and median regression through
(qua.regressCOP, qua.regress2COP, med.regressCOP,
med.regress2COP) for a given copula where "2" represents V with
respect to U instead of U with respect to V. The regressions
can be plotted by (qua.regressCOP.draw).
Maintainer: William H. Asquith <william.asquith@ttu.edu>
Depends: lmomco
License: GPL
Packaged: 2011-02-18 19:19:05 UTC; wasquith
Repository: CRAN
Date/Publication: 2011-02-19 09:06:54