# General Bivariate Copula Theory and Many Utility Functions

## Documentation for package ‘copBasic’ version 2.2.15

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

## Help Pages

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

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

## -- A --

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

## -- B --

bicCOP | Bayesian Information Criterion between a Fitted Coupla and an Empirical Copula
bicoploc | Analog to Line of Organic Correlation by Copula Diagonal
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
breveCOP | Add Asymmetry to a Copula

## -- C --

CIRCcop | Copula of Circular Uniform Distribution
CLcop | The Clayton Copula
coCOP | The Co-Copula Function
composite1COP | Composition of a Single Symmetric Copula with Two Compositing Parameters (Khoudraji Device with Pi Independence)
composite2COP | Composition of Two Copulas with Two Compositing Parameters (Khoudraji Device)
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
EMPIRgrid_fast | Fast Grid of the Bivariate Empirical Copula
EMPIRgrid_lkup | Empirical Copula by Bilinear Interpolation of Gridded Bivariate Empirical Copula
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
EuvCOP | Expected value of U given V
EvuCOP | Expected value of V given U

## -- F --

FGMcop | The Generalized Farlie-Gumbel-Morgenstern Copula
FGMicop | The Generalized Farlie-Gumbel-Morgenstern Copula
footCOP | The Spearman Footrule of a Copula
FRcop | The Frank 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 --

HAIRPINcop | The Hairpin Copula
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
JOMAcop | The Joe-Ma 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
kfuncCOP_Pd | The Kendall (Distribution) Function of d-Dimensional Independence Copula
khoudraji1COP | Composition of a Single Symmetric Copula with Two Compositing Parameters (Khoudraji Device with Pi Independence)
khoudraji2COP | Composition of Two Copulas with Two Compositing Parameters (Khoudraji Device)
khoudrajiPCOP | Composition of a Single Symmetric Copula with Two Compositing Parameters (Khoudraji Device with Pi Independence)
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
LCOMDIA_GH2cop | L-comoment Ratio Diagrams for 2-Parameter Gumbel-Hougaard Extreme Value Copula
LCOMDIA_GH3cop | L-comoment Ratio Diagrams for 3-Parameter Gumbel-Hougaard Extreme Value Copula
LCOMDIA_ManyCops | L-comoment Ratio Diagrams for Many Copulas
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
LMRuvCOP | Conditional L-moments of the Distribution of U given V
LMRvuCOP | Conditional L-moments of the Distribution of V given U
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)
LzCOPpermsym | Maximum Asymmetry Measure (or Vector) of a Copula by Exchangeability (Permutation Symmetry)

## -- 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
MOcop | The Marshall-Olkin Copula
M_N5p12b | Shuffles of Upper-Bound Copula, Example 5.12b of Nelsen's Book

## -- N --

N4212cop | The Copula of Equation 4.2.12 of Nelsen's Book
N4220cop | The Copula of Equation 4.2.20 of Nelsen's Book
NORMcop | The Normal (Gaussian) Copula
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

## -- O --

ORDSUMcop | Ordinal Sums of M-Copula
ORDSUWcop | Ordinal Sums of W-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 --

RAYcop | The Rayleigh Copula
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 | Root Mean Square Error between a Fitted Copula and an Empirical Copula
rN4220cop | The (Reflected) Copula of Equation 4.2.20 of Nelsen's Book

## -- 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
Tcop | The t-Student Copula
tEVcop | The t-EV (Extreme Value) Copula
TRIcop | The Triangular 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 | Schweizer and Wolff Sigma of a Copula
wolfCOPsamc | Monte Carlo Integration of Schweizer-Wolff Sigma
wolfCOPtest | Empirically Created Schweizer and Wolff Sigma Test Against an Independence Copula
wolfCOPtest_data_smlsam | Small Sample Components for Schweizer-Wolff Sigma Test
W_N5p12a | Ordinal Sums of Lower-Bound Copula, Example 5.12a of Nelsen's Book