copBasic: General Bivariate Copula Theory and Many Utility Functions
Extensive functions for bivariate copula (bicopula) computations and related mathematical operations oriented around the oft cited and fundamental bicopula theory described by Nelsen (2006), Joe (2014), and other selected works. The lower, upper, product, and a few select other bicopula are implemented. Individual copula support is deliberately limited to keep the package focused on an educational API to major bicopula theory. Expressions for an arbitrary bicopula include the diagonal, survival copula, the dual of a copula, co-copula, and numerical bicopula density. Level curves (sets) as well as horizontal and vertical sections and derivatives of such sections also are supported. The numerical derivatives of a bicopula are provided as well as inverses; simulation by the conditional distribution method thus are supported. Composition, convex combination, and products of bicopula are provided. Copula properties include Kendall Function and L-moments thereof, Kendall Tau, Spearman Rho and Footrule, Gini Gamma, Blomqvist Beta, Hoeffding Phi, Schweizer-Wolff Sigma, tail dependency and order, and skewness. Evaluators of positively/negatively quadrant dependency, left-tail decreasing, and right-tail increasing are available. Kullback-Leibler divergence, Vuong's procedure, and L-comoments for copula inference are available. Quantile and median regressions for V with respect to U and U with respect to V are available. Empirical copulas (EC) are supported.