Basic Theoretical Copula, Empirical Copula, and Various Utility
Functions
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,
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.