# General Bivariate Copula Theory and Many Utility Functions

## Documentation for package ‘copBasic’ version 2.0.7

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D E F G H I J K L M N P Q R S T U V W

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

## -- A --

asCOP | A Wrapper on a User-Level Formula to Become a Copula Function

## -- B --

bilmoms | Bivariate L-moments and L-comoments of a Copula
blomCOP | The Blomqvist's Beta 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's 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 | Dataframe of the Bivariate Emprical Copula
EMPIRgrid | Grid of the Bivariate Emprical Copula
EMPIRgridder | Derivatives of the Grid of the Bivariate Emprical Copula for V with respect to U
EMPIRgridder2 | Derivatives of the Grid of the Bivariate Emprical Copula for U with respect to V
EMPIRgridderinv | Derivative Inverses of the Grid of the Bivariate Emprical Copula for V with respect to U
EMPIRgridderinv2 | Derivative Inverses of the Grid of the Bivariate Emprical Copula for U with respect to V
EMPIRmed.regress | Median Regression of the Grid of the Bivariate Emprical Copula for V with respect to U
EMPIRmed.regress2 | Median Regression of the Grid of the Bivariate Emprical Copula for U with respect to V
EMPIRqua.regress | Quantile Regression of the Grid of the Bivariate Emprical Copula for V with respect to U
EMPIRqua.regress2 | Quantile Regression of the Grid of the Bivariate Emprical 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 --

footCOP | The Spearman's Footrule of a Copula
FRECHETcop | The Fréchet Family Copula

## -- G --

GHcop | The Gumbel-Hougaard Extreme Value Copula
giniCOP | The Gini's Gamma of a Copula
GLcop | The Galambos Extreme Value Copula
gridCOP | Compute a Copula on a Grid

## -- H --

hoefCOP | The Hoeffding's 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 --

joeskewCOP | The Joe's Nu-Skew or Nu-Skew-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's Divergence, and Kullback-Leibler Sample Size
kullCOPint | Kullback-Leibler Divergence, Jeffrey's Divergence, and Kullback-Leibler Sample Size

## -- L --

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's Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms)
LpCOPpermsym | The Hoeffding's Phi of a Copula or Lp Distances (Independence, Radial Asymmetry, or Reflection Symmetry Forms)
LpCOPradsym | The Hoeffding's 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 | The Joe's Nu-Skew or Nu-Skew-Star of a Copula
nustarCOP | The Joe's Nu-Skew or Nu-Skew-Star of a Copula

## -- P --

P | The Product (Independence) 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
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's Rho of a Copula

## -- S --

sectionCOP | The Sections or Derivative of the Sections of a Copula
semicorCOP | The Lower and Upper Semi-Correlations of a Copula
simcomposite2COP | Compute the L-comoments of a Two-Value Composited Copula by Numerical Simulation
simcomposite3COP | Compute the L-comoments of a Four-Value Composited Copula by Numerical Simulation
simcompositeCOP | Compute the L-comoments of a Two-Value Composited Copula by Numerical 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 the 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's Tau and Concordance Function of a 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 | Vuong's Procedure for Parametric Copula Comparison

## -- W --

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