copBasic: Basic Theoretical Copula, Empirical Copula, and Various Utility Functions

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, upper, product, "PSP," and Plackett copulas. Plackett parameter estimation is provided. Expressions available for an arbitrary copula include the diagonal of a copula, the survival copula, the dual of a copula, and co-copula. Levels curves, such as for drawing, are available, through inverses of copulas. Sections (horizontal and vertical) and derivatives of these sections are supported. The numerical derivative for the derivative of a copula is provided as are inverses of these the numerical derivatives. Inverses of copula derivatives are important for random variate generation, which is provided using the conditional distribution method and the derivative of a copula. Composition of a single copula for two external parameters, composition of two copulas through use of two external parameters, and the composition of two copulas through the use of four external parameters is provided. Composite copula random variates can be generated—compositions generally yield asymmetric copulas. A data set is provided that contains darts thrown at the L-comoment space of a Plackett-Plackett composited copula; these data might be used for experimental copula estimation by the method of L-comoments. Measures of association through concordance include Kendall Tau, Spearman Rho, Gini Gamma, and Blomqvist Beta. Schweizer-Wolff Sigma is provided as a measure of dependency in contrast to the concordance measures. Upper- and lower-tail dependence is computed by numerical limit convergence. Whether a copula is left-tail decreasing or right-tail increasing also is provided. Quantile and median regression for V with respect to U and U with respect to V is available. Empirical copulas (EC) are supported and the computation of a data frame for each sample value also is provided. ECs are heavily dependent on a simple grid or matrix structure for which generation capability is provided. The derivatives of the EC grid, which are the conditional CDFs of copula sections, are computable. Also, the inverses of the derivatives, which are the conditional QDFs of copula sections are computable. Median and quantile regression of an EC is supported. Lastly, support for EC simulation of V conditional on U is provided.

Version: 1.5.4
Depends: R (≥ 2.10), lmomco
Published: 2013-05-10
Author: William H. Asquith
Maintainer: William H. Asquith <william.asquith at>
License: GPL-2 | GPL-3 [expanded from: GPL]
NeedsCompilation: no
Materials: ChangeLog
In views: Distributions
CRAN checks: copBasic results


Reference manual: copBasic.pdf
Package source: copBasic_1.5.4.tar.gz
MacOS X binary: copBasic_1.5.4.tgz
Windows binary:
Old sources: copBasic archive

Reverse dependencies:

Reverse suggests: lmomco