Package: copBasic
Title: Basic Theoretical Copula, Empirical Copula, and Various Utility
        Functions
Version: 1.5.1
Date: 2011-11-14
Author: William H. Asquith
Description: This package implements extensive, but select, 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 a single copula for two external
        parameters is by (composite1COP). Composition of two copulas
        through use of two external parameters is provided by
        (composite2COP), and the composition of two copulas through the
        use of four external parameters is provided by (composite3COP).
        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). **Empirical Copulas**
        Empirical copulas are supported by (EMPIRcop) and the
        computation of a data frame of the copula for each sample value
        is provided by (EMPIRcopdf). The empirical copula functions are
        heavily dependent on a simple grid or matrix structure, which
        is created by (EMPIRgrid). The derivatives of the grid, which
        are the conditional cumulative distribution functions of the
        copula sections, are computed by (EMPIRgridder and
        EMPIRgridder2). The inverses of the derivatives, which are the
        conditional quantile functions of the copula sections, are
        computed by (EMPIRgridderinv and EMPIRgridderinv2). Support for
        median and quantile regression of the empricial copula are
        provided by (EMPIRmed.regress, EMPIRmed.regress2,
        EMPIRqua.regress, EMPIRqua.regress2), which use the grids
        emanating from (EMPIRgridderinv and EMPIRgridderinv2). Support
        for simulation of V using U from an empirical copula is
        provided by (EMPIRsim or by EMPIRsimv).
Maintainer: William H. Asquith <william.asquith@ttu.edu>
Depends: R (>= 2.10), lmomco
License: GPL
Packaged: 2011-12-06 15:07:14 UTC; williamasquith
Repository: CRAN
Date/Publication: 2011-12-06 17:09:21
Built: R 2.13.2; ; 2011-12-07 19:07:41 UTC; windows
