Basic Theoretical Copula, Empirical Copula, and Various Utility
Functions
Description
The package implements extensive functions for copula computations and related mathematical operations oriented around the oft cited and fundamental copula theory described by Nelson (2006). The lower (W), upper (M), product (P), PSP, and Plackett (with parameter estimation) copulas are provided. Individual copula functional support is intentionally limited to keep the package focused on an API to general copula theory. Expressions available for an arbitrary copula include the diagonal of a copula, the survival copula, the dual of a copula, and co-copula. Level curves (sets) are available. Horizontal and vertical copula sections and derivatives of such sections also are supported. The numerical derivatives of a copula are provided as well as inverses, and thus functions for copula simulation also are supported. Composition of copulas is provided: (1) composition of a single copula using two composition parameters, (2) composition of two copulas using two composition parameters, (3) composition of two copulas using four composition parameters, and (4) composite copula random variates. Characteristics of copulas include Kendall Tau, Spearman Rho, Gini Gamma, Blomqvist Beta, and Schweizer-Wolff Sigma. Logical evaluators of positively/negatively quadrant dependency, left-tail decreasing, and right-tail increasing also are available. Quantile and median regression for V with respect to U and U with respect to V is available. Empirical copulas (EC) are supported. ECs are dependent on gridded data structures for which generation capability is provided. The derivatives of the EC grid are computable. Also, the inverses of the derivatives, which are the conditional QDFs of copula sections also are computable. Median and quantile regression of an EC also is supported along with support for EC simulation of V conditional on U.