copBasic: General Bivariate Copula Theory and Many Utility Functions
Extensive functions for bivariate copula (bicopula) computations and related operations concerning oft cited bicopula theory described by Nelsen (2006), Joe (2014), and other selected works. The lower, upper, product, and select other bicopula are implemented. Individual copula support is deliberately limited to keep the package focused on an API to bicopula theory. Arbitrary bicopula expressions include the diagonal, survival copula, the dual of a copula, co-copula, numerical bicopula density, and maximum likelihood estimation. Level curves/sets, horizontal/vertical sections also are supported. Numerical derivatives and inverses of a bicopula are provided; simulation by the conditional distribution method thus is supported. Bicopula Ccomposition, convex combination, and products are provided. Support extends to Kendall Function and L-moments thereof, Kendall Tau, Spearman Rho and Footrule, Gini Gamma, Blomqvist Beta, Hoeffding Phi, Schweizer-Wolff Sigma, tail dependency (including pseudo-polar representation) and tail order, skewness, and bivariate L-moments. Evaluators of positively/negatively quadrant dependency, left(right)-tail decreasing(increasing) are available. Kullback-Leibler divergence, Vuong's procedure, Spectral Measure, 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.
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