# General Bivariate Copula Theory and Many Utility Functions ## Help Pages

 copBasic-package Basic Theoretical Copula, Empirical Copula, and Various Utility Functions

## -- A --

 aicCOP The Akaike Information Criterion between a Fitted Coupla and an Empirical Copula AMHcop The Ali-Mikhail-Haq Copula asCOP A Wrapper on a User-Level Formula to Become a Copula Function

## -- B --

 bicCOP The Bayesian Information Criterion between a Fitted Coupla and an Empirical Copula bilmoms Bivariate L-moments and L-comoments of a Copula blomatrixCOP A Matrix of Blomqvist-like Betas of a Copula blomatrixCOPdec A Matrix of Blomqvist-like Betas of a Copula blomatrixCOPiqr A Matrix of Blomqvist-like Betas of a Copula blomCOP The Blomqvist Beta of a Copula blomCOPss Blomqvist (Schmid-Schmidt) Betas of a Copula

## -- C --

 CLcop The Clayton Copula coCOP The Co-Copula Function composite1COP Composition of a Single Symmetric Copula with Two Compositing Parameters composite2COP Composition of Two Copulas with Two Compositing Parameters composite3COP (Extended) Composition of Two Copulas with Four Compositing Parameters concordCOP The Kendall Tau and Concordance Function of a Copula convex2COP Convex Combination of Two Copulas convexCOP Convex Combination of an Arbitrary Number of Copulas COP The Copula copBasic.fitpara.beta A Single or Multi-Parameter Optimization Engine (Beta Version) COPinv The Inverse of a Copula for V with respect to U COPinv2 The Inverse of a Copula for U with respect to V

## -- D --

 densityCOP Density of a Copula densityCOPplot Contour Density Plot of a Copula derCOP Numerical Derivative of a Copula for V with respect to U derCOP2 Numerical Derivative of a Copula for U with respect to V derCOPinv Numerical Derivative Inverse of a Copula for V with respect to U derCOPinv2 Numerical Derivative Inverse of a Copula for U with respect to V diagCOP The Diagonals of a Copula diagCOPatf Numerical Rooting the Diagonal of a Copula diagCOPinv Numerical Rooting the Diagonal of a Copula duCOP The Dual of a Copula Function

## -- E --

 EMPIRcop The Bivariate Empirical Copula EMPIRcopdf Data Frame Representation of the Bivariate Empirical Copula EMPIRgrid Grid of the Bivariate Empirical Copula EMPIRgridder Derivatives of the Grid of the Bivariate Empirical Copula for V with respect to U EMPIRgridder2 Derivatives of the Grid of the Bivariate Empirical Copula for U with respect to V EMPIRgridderinv Derivative Inverses 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 EMPIRmed.regress2 Median Regression of the Grid of the Bivariate Empirical Copula for U with respect to V EMPIRqua.regress Quantile 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 EMPIRsim Simulate a Bivariate Empirical Copula EMPIRsimv Simulate a Bivariate Empirical Copula For a Fixed Value of U

## -- F --

 FGMcop The Generalized Farlie-Gumbel-Morgenstern Copula FGMicop The Generalized Farlie-Gumbel-Morgenstern Copula footCOP The Spearman Footrule of a Copula FRECHETcop The Fréchet Family Copula

## -- G --

 gEVcop The Gaussian-based (Extreme Value) Copula GHcop The Gumbel-Hougaard Extreme Value Copula giniCOP The Gini Gamma of a Copula GLcop The Galambos Extreme Value Copula (with Gamma Power Mixture [Joe/BB4] and Lower Extreme Value Limit) GLEVcop The Galambos Extreme Value Copula (with Gamma Power Mixture [Joe/BB4] and Lower Extreme Value Limit) GLPMcop The Galambos Extreme Value Copula (with Gamma Power Mixture [Joe/BB4] and Lower Extreme Value Limit) glueCOP Gluing Two Copulas gridCOP Compute a Copula on a Grid

## -- H --

 hoefCOP The Hoeffding Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms) HRcop The Hüsler-Reiss Extreme Value Copula

## -- I --

 isCOP.LTD Is a Copula Left-Tail Decreasing isCOP.permsym Is a Copula Permutation Symmetric isCOP.PQD The Positively Quadrant Dependency State of a Copula isCOP.radsym Is a Copula Radially Symmetric isCOP.RTI Is a Copula Right-Tail Increasing isfuncCOP Is a General Bivariate Function a Copula by Gridded Search?

## -- J --

 JOcopB5 The Joe/B5 Copula (B5) JOcopBB4 The Galambos Extreme Value Copula (with Gamma Power Mixture [Joe/BB4] and Lower Extreme Value Limit) joeskewCOP Joe's Nu-Skew and the copBasic Nu-Star of a Copula joint.curvesCOP Compute Coordinates of the Marginal Probabilities given joint AND or OR Probabilities joint.curvesCOP2 Compute Coordinates of the Marginal Probabilities given joint AND or OR Probability jointCOP Compute Equal Marginal Probabilities Given a Single Joint AND or OR Probability for a Copula

## -- K --

 kfuncCOP The Kendall (Distribution) Function of a Copula kfuncCOPinv The Inverse Kendall Function of a Copula kfuncCOPlmom The L-moments of the Kendall Function of a Copula kfuncCOPlmoms The L-moments of the Kendall Function of a Copula kmeasCOP The Kendall (Distribution) Function of a Copula kullCOP Kullback-Leibler Divergence, Jeffrey Divergence, and Kullback-Leibler Sample Size kullCOPint Kullback-Leibler Divergence, Jeffrey Divergence, and Kullback-Leibler Sample Size

## -- L --

 lcomCOP L-comoments and Bivariate L-moments of a Copula lcomCOPpv Simulating the Sample Distribution(s) of L-correlation, L-coskew, and L-cokurtosis for a Copula lcomoms2.ABcop2parameter Convert L-comoments to Parameters of Alpha-Beta Compositions of Two One-Parameter Copulas lcomoms2.ABKGcop2parameter Convert L-comoments to Parameters of Alpha-Beta-Kappa-Gamma Compositions of Two One-Parameter Copulas level.curvesCOP Compute and Plot Level Curves of a Copula V with respect to U level.curvesCOP2 Compute and Plot Level Curves of a Copula U with respect to V level.setCOP Compute a Level Set of a Copula V with respect to U level.setCOP2 Compute a Level Set of a Copula U with respect to V LpCOP The Hoeffding Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms) LpCOPpermsym The Hoeffding Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms) LpCOPradsym The Hoeffding Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms)

## -- M --

 M The Fréchet-Hoeffding Upper Bound Copula med.regressCOP Perform Median Regression using a Copula by Numerical Derivative Method for V with respect to U med.regressCOP2 Perform Median Regression using a Copula by Numerical Derivative Method for U with respect to V mleCOP Maximum Pseudo-Log-Likelihood Estimation for Copula Parameter Estimation

## -- N --

 N4212cop The Copula of Equation 4.2.12 of Nelsen's Book nuskewCOP Joe's Nu-Skew and the copBasic Nu-Star of a Copula nustarCOP Joe's Nu-Skew and the copBasic Nu-Star of a Copula

## -- P --

 P The Product (Independence) Copula PAcop The Pareto Copula PARETOcop The Pareto Copula PLACKETTcop The Plackett Copula PLACKETTpar Estimate the Parameter of the Plackett Copula PLACKETTsim Direct Simulation of a Plackett Copula PLcop The Plackett Copula PLpar Estimate the Parameter of the Plackett Copula prod2COP The Product of Two Copulas psepolar Pseudo-Polar Representation of Bivariate Data PSP The Ratio of the Product Copula to Summation minus Product Copula

## -- Q --

 qua.regressCOP 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 qua.regressCOP2 Perform Quantile Regression using a Copula by Numerical Derivative Method for U with respect to V

## -- R --

 rCOP Simulate a Copula by Numerical Derivative Method ReineckeWell266 Porosity and Permeability Data for Well-266 of the Reinecke Oil Field, Horseshoe Atoll, Texas ReineckeWells Porosity and Permeability Data for the Reinecke Oil Field, Horseshoe Atoll, Texas RFcop The Raftery Copula rhobevCOP 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 rhoCOP The Spearman Rho of a Copula rmseCOP The Root Mean Square Error between a Fitted Copula and an Empirical Copula

## -- S --

 sectionCOP The Sections or Derivative of the Sections of a Copula semicorCOP Lower and Upper Semi-Correlations of a Copula simcomposite2COP Compute the L-comoments of a Two-Value Composited Copula by Simulation simcomposite3COP Compute the L-comoments of a Four-Value Composited Copula by Simulation simcompositeCOP Compute the L-comoments of a Two-Value Composited Copula by Simulation simCOP Simulate a Copula by Numerical Derivative Method simCOPmicro Simulate V from U through a Copula by Numerical Derivative Method simCOPv Simulate V from U through a Copula by Numerical Derivative Method spectralmeas Estimation of the Spectral Measure stabtaildepf Estimation of the Stable Tail Dependence Function statTn The Tn Statistic of a Fitted Copula to an Empirical Copula surCOP The Survival Copula surfuncCOP The Joint Survival Function

## -- T --

 tailconCOP The Tail Concentration Function of a Copula taildepCOP The Lower- and Upper-Tail Dependency Parameters of a Copula tailordCOP The Lower- and Upper-Tail Orders of a Copula tauCOP The Kendall Tau and Concordance Function of a Copula tEVcop The t-EV (Extreme Value) Copula

## -- U --

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

## -- V --

 vuongCOP The Vuong Procedure for Parametric Copula Comparison

## -- W --

 W The Fréchet-Hoeffding Lower Bound Copula wolfCOP The Schweizer and Wolff Sigma of a Copula