# This text file contains the original DESCRIPTION (will after many versions)
# for which CRAN maintainer's reasonably critiqued as being too long.
# In May 2013, a new DESCRIPTION was written as a contraction of this file.
# However, because the description here actually ties in the functions of the
# package, it was decided to add this file to the sources of copBasic.

Package: copBasic
Title: Basic Theoretical Copula, Empirical Copula, and Various Utility Functions
Author: William H. Asquith

Description: The copBasic package implements extensive functions for copula computations. copBasic 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 appended "2" to copBasic functions represents V with respect to U instead of U with respect to V. The numerical derivative for the derivative of a copula is provided (derCOP and derCOP2) and the inversion of those functions (derCOPinv and derCOPinv2). The diagonal sections of a copula are supported (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 derivative of a copula is provided (simCOP and reduced features in the faster simCOPmicro). Composition of a single copula for two external parameters is supported (composite1COP). Composition of two copulas through use of two external parameters is supported (composite2COP), and lastly, the composition of two copulas through the use of four external parameters is supported (composite3COP). Composite copula random variates are supported (simcompositeCOP). Copula compositions generally yield asymmetric to highly asymmetric copulas.

copBasic also provides a full suite of functions to numerically compute measures of association through concordance measures 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 in contrast to the concordance measures. Upper- and lower-tail dependence is computed by numerical limit convergence (taildepCOP). A numerical computation of a logical response as to whether a copula is left-tail decreasing or right-tail increasing is provided (isCOP.LTD and isCOP.RTI). The package supports quantile and median regression through (qua.regressCOP, qua.regress2COP, med.regressCOP, med.regress2COP) for a give copula. The regressions can be plotted by (qua.regressCOP.draw). 


For slightly broader application for purposes of education and experimentation with copulas, copBasic 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). 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. This method remains untapped within the literature as of March 2013.


Empirical copulas are supported (EMPIRcop) and the computation of a data frame of the copula for each sample value is provided (EMPIRcopdf). The empirical copula functions are heavily dependent on a simple grid or matrix structure, which is created (EMPIRgrid). The derivatives of the grid, which are the conditional cumulative distribution functions of the copula sections, are computed (EMPIRgridder and EMPIRgridder2). The inverses of the derivatives, which are the conditional quantile functions of the copula sections, are computable (EMPIRgridderinv and EMPIRgridderinv2). Support for median and quantile regression of the empirical copula are provided (EMPIRmed.regress, EMPIRmed.regress2, EMPIRqua.regress, EMPIRqua.regress2), which use the grids from (EMPIRgridderinv and EMPIRgridderinv2). Support for simulation of V using U from an empirical copula is provided (EMPIRsim or EMPIRsimv).


