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copBasic (version 2.2.15)

General Bivariate Copula Theory and Many Utility Functions

Description

Extensive functions for bivariate copula (bicopula) computations and related operations for bicopula theory. The lower, upper, product, and select other bicopula are implemented along with operations including the diagonal, survival copula, dual of a copula, co-copula, and numerical bicopula density. Level sets, horizontal and vertical sections are supported. Numerical derivatives and inverses of a bicopula are provided through which simulation is implemented. Bicopula composition, convex combination, asymmetry extension, and products also are provided. Support extends to the Kendall Function as well as the Lmoments thereof. Kendall Tau, Spearman Rho and Footrule, Gini Gamma, Blomqvist Beta, Hoeffding Phi, Schweizer- Wolff Sigma, tail dependency, tail order, skewness, and bivariate Lmoments are implemented, and positive/negative quadrant dependency, left (right) increasing (decreasing) are available. Other features include Kullback-Leibler Divergence, Vuong Procedure, spectral measure, and Lcomoments for fit and inference, Lcomoment ratio diagrams, maximum likelihood, and AIC, BIC, and RMSE for goodness-of-fit.

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Install

install.packages('copBasic')

Monthly Downloads

993

Version

2.2.15

License

GPL-2

Maintainer

William Asquith

Last Published

July 22nd, 2026

Functions in copBasic (2.2.15)

Derivatives of the Grid of the Bivariate Empirical Copula for V with respect to U

EMPIRgridderinv

Derivative Inverses of the Grid of the Bivariate Empirical Copula for V with respect to U

Empirical Copula by Bilinear Interpolation of Gridded Bivariate Empirical Copula

Derivatives of the Grid of the Bivariate Empirical Copula for U with respect to V

Simulate a Bivariate Empirical Copula

EMPIRqua.regress

Quantile Regression of the Grid of the Bivariate Empirical Copula for V with respect to U

EMPIRgridderinv2

Derivative Inverses of the Grid of the Bivariate Empirical Copula for U with respect to V

EMPIRmed.regress

Median Regression of the Grid of the Bivariate Empirical Copula for V with respect to U

EMPIRqua.regress2

Quantile Regression of the Grid of the Bivariate Empirical Copula for U with respect to V

EMPIRmed.regress2

Median Regression of the Grid of the Bivariate Empirical Copula for U with respect to V

Simulate a Bivariate Empirical Copula For a Fixed Value of U

The Fréchet Family Copula

The Hairpin Copula

The Hüsler--Reiss Extreme Value Copula

The Frank Copula

The Generalized Farlie--Gumbel--Morgenstern Copula

The Gumbel--Hougaard Extreme Value Copula

The Galambos Extreme Value Copula (with Gamma Power Mixture [Joe/BB4] and Lower Extreme Value Limit)

Expected value of U given V

Expected value of V given U

The Marshall--Olkin Copula

The Fréchet--Hoeffding Upper-Bound Copula

L-comoment Ratio Diagrams for 2-Parameter Gumbel--Hougaard Extreme Value Copula

L-comoment Ratio Diagrams for 3-Parameter Gumbel--Hougaard Extreme Value Copula

LCOMDIA_ManyCops

L-comoment Ratio Diagrams for Many Copulas

Conditional L-moments of the Distribution of U given V

The Joe--Ma Copula

Maximum Asymmetry Measure (or Vector) of a Copula by Exchangeability (Permutation Symmetry)

Conditional L-moments of the Distribution of V given U

The Joe/B5 Copula (B5)

The Plackett Copula

The Copula of Equation 4.2.12 of Nelsen's Book

Ordinal Sums of W-Copula

Shuffles of Upper-Bound Copula, Example 5.12b of Nelsen's Book

The Normal (Gaussian) Copula

The Copula of Equation 4.2.20 of Nelsen's Book

The Product (Independence) Copula

The Pareto Copula

Estimate the Parameter of the Plackett Copula

Ordinal Sums of M-Copula

The t-Student Copula

The Rayleigh Copula

Porosity and Permeability Data for the Reinecke Oil Field, Horseshoe Atoll, Texas

ReineckeWell266

Porosity and Permeability Data for Well-266 of the Reinecke Oil Field, Horseshoe Atoll, Texas

The Triangular Copula

Direct Simulation of a Plackett Copula

The Fréchet--Hoeffding Lower-Bound Copula

The Raftery Copula

Ordinal Sums of Lower-Bound Copula, Example 5.12a of Nelsen's Book

The Ratio of the Product Copula to Summation minus Product Copula

Analog to Line of Organic Correlation by Copula Diagonal

Wrapper on a User-Level Formula to Become a Copula Function

A Matrix of Blomqvist-like Betas of a Copula

The Blomqvist Beta of a Copula

Akaike Information Criterion between a Fitted Coupla and an Empirical Copula

The Co-Copula Function

Blomqvist (Schmid--Schmidt) Betas of a Copula

Bayesian Information Criterion between a Fitted Coupla and an Empirical Copula

Add Asymmetry to a Copula

Bivariate L-moments and L-comoments of a Copula

(Extended) Composition of Two Copulas with Four Compositing Parameters

Convex Combination of an Arbitrary Number of Copulas

Convex Combination of Two Copulas

Numerical Derivative of a Copula for V with respect to U

Contour Density Plot of a Copula

Density of a Copula

Composition of a Single Symmetric Copula with Two Compositing Parameters (Khoudraji Device with Pi Independence)

copBasic.fitpara

A Single or Multi-Parameter Optimization Engine (Beta Version)

Composition of Two Copulas with Two Compositing Parameters (Khoudraji Device)

copBasic-package

Basic Theoretical Copula, Empirical Copula, and Various Utility Functions

The Spearman Footrule of a Copula

Numerical Derivative Inverse of a Copula for U with respect to V

Numerical Rooting the Diagonal of a Copula

Numerical Derivative Inverse of a Copula for V with respect to U

The Gini Gamma of a Copula

Numerical Derivative of a Copula for U with respect to V

Gluing Two Copulas

The Dual of a Copula Function

The Gaussian-based (Extreme Value) Copula

The Diagonals of a Copula

Is a Copula Radially Symmetric

Is a General Bivariate Function a Copula by Gridded Search?

joint.curvesCOP

Compute Coordinates of the Marginal Probabilities given joint AND or OR Probabilities

Is a Copula Right-Tail Increasing

The Positively Quadrant Dependency State of a Copula

Is a Copula Permutation Symmetric

The Hoeffding Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms)

Compute a Copula on a Grid

Joe's Nu-Skew and the copBasic Nu-Star of a Copula

Is a Copula Left-Tail Decreasing

L-comoments and Bivariate L-moments of a Copula

Compute Equal Marginal Probabilities Given a Single Joint AND or OR Probability for a Copula

The Inverse Kendall Function of a Copula

Simulating the Sample Distribution(s) of L-correlation, L-coskew, and L-cokurtosis for a Copula

lcomoms2.ABKGcop2parameter

Convert L-comoments to Parameters of Alpha-Beta-Kappa-Gamma Compositions of Two One-Parameter Copulas

The Kendall (Distribution) Function of d-Dimensional Independence Copula

Kullback--Leibler Divergence, Jeffrey Divergence, and Kullback--Leibler Sample Size

joint.curvesCOP2

Compute Coordinates of the Marginal Probabilities given joint AND or OR Probability

The Kendall (Distribution) Function of a Copula

The L-moments of the Kendall Function of a Copula

level.curvesCOP2

Compute and Plot Level Curves of a Copula U with respect to V

Pseudo-Polar Representation of Bivariate Data

lcomoms2.ABcop2parameter

Convert L-comoments to Parameters of Alpha-Beta Compositions of Two One-Parameter Copulas

level.curvesCOP

Compute and Plot Level Curves of a Copula V with respect to U

med.regressCOP2

Perform Median Regression using a Copula by Numerical Derivative Method for U with respect to V

Maximum Pseudo-Log-Likelihood Estimation for Copula Parameter Estimation

Compute a Level Set of a Copula U with respect to V

The Product of Two Copulas

Compute a Level Set of a Copula V with respect to U

Perform Median Regression using a Copula by Numerical Derivative Method for V with respect to U

The Sections or Derivative of the Sections of a Copula

Perform Quantile Regression using a Copula by Numerical Derivative Method for V with respect to U

qua.regressCOP.draw

Draw Quantile Regressions using a Copula by Numerical Derivative Method for V with respect to U or U with respect to V

Root Mean Square Error between a Fitted Copula and an Empirical Copula

Lower and Upper Semi-Correlations of a Copula

Simulate a Copula by Numerical Derivative Method

A Dependence Measure for a Bivariate Extreme Value Copula based on the Expectation of the Product of Negated Log-Transformed Random Variables U and V

The Spearman Rho of a Copula

qua.regressCOP2

Perform Quantile Regression using a Copula by Numerical Derivative Method for U with respect to V

The (Reflected) Copula of Equation 4.2.20 of Nelsen's Book

simcompositeCOP

Compute the L-comoments of a Two-Value Composited Copula by Simulation

Estimation of the Spectral Measure

The Tail Concentration Function of a Copula

Estimation of the Stable Tail Dependence Function

The Joint Survival Function

Simulate V from U through a Copula by Numerical Derivative Method

The Tn Statistic of a Fitted Copula to an Empirical Copula

simcomposite3COP

Compute the L-comoments of a Four-Value Composited Copula by Simulation

The t-EV (Extreme Value) Copula

The Survival Copula

wolfCOPtest_data_smlsam

Small Sample Components for Schweizer--Wolff Sigma Test

Monte Carlo Integration of Schweizer--Wolff Sigma

Bivariate Skewness after Joe (2014) or the Univariate L-moments of Combined U and V

Empirically Created Schweizer and Wolff Sigma Test Against an Independence Copula

The Lower- and Upper-Tail Dependency Parameters of a Copula

The Vuong Procedure for Parametric Copula Comparison

The Lower- and Upper-Tail Orders of a Copula

The Kendall Tau and Concordance Function of a Copula

Schweizer and Wolff Sigma of a Copula

Data Frame Representation of the Bivariate Empirical Copula

The Clayton Copula

Copula of Circular Uniform Distribution

Grid of the Bivariate Empirical Copula

The Inverse of a Copula for U with respect to V

The Inverse of a Copula for V with respect to U

Fast Grid of the Bivariate Empirical Copula

The Ali--Mikhail--Haq Copula

The Bivariate Empirical Copula