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copBasic (version 1.5.0)

Basic Copula Functions

Description

This package implements basic functions for copula computations and is used by several other packages by the author. This particular package provides the lower (W), upper (M), and product (P) copulas as well as the product-summation-product copula (PSP). Wrapper functions for the copula (COP), survival copula (surCOP), dual of a copula (duCOP), and co-copula (coCOP) are provided. The package has (level.curvesCOP) for drawing level curves of a given copula, and this function uses the inverse of a copula (COPinv and a COPinv2 is provided for completeness). The numerical derivative for the derivative of a copula is provided by (derCOP and derCOP2) and the inversion of these functions are by (derCOPinv and derCOPinv2). The diagonal sections of a copula are supported by (diagCOP), and sections and derivatives of sections are supported by (sectionCOP). The inverses of copula derivatives are important for random variate generation. Random variate generation for a copula using the conditional distribution method and the deriviative of a copula is provided by (simCOP and the reduced capability simCOPmicro). For slightly broader application for purposes of education and experimentation with copulas, this package also supports the Plackett copula (PLACKETTcop) because of the general applicability of this copula. The Plackett copula is comprehensive, which means that it can attain complete negative association, independence, and positive association. Plackett parameter estimation is straightforward with (PLACKETTpar). A Plackett-specific, random-variate algorithm is by (PLACKETTsim). Composition of two copulas is provided by (composite2COP), and composition of one copula is provided by function (composite1COP). Composite copula random variates are generated by (simcompositeCOP). These compositions generally yield asymmetric copulas. A data set is provided that contains darts thrown at the L-comoment space of a Plackett-Plackett composited compula; these data might be used for experimental copula estimation by the method of L-comoments. The package also provides a full suite of functions to numerically compute measures of association through concordance for a given copula such as Kendall's Tau (tauCOP), Spearman's Rho (rhoCOP), Gini's Gamma (giniCOP), and Blomqvist's Beta (blomCOP). The Schweizer and Wolff's Sigma (wolfCOP) is implemented as a measure of dependency as opposed the the concordance measures just listed. Upper and lower tail dependence is computed by numerical limit convergence by (taildepCOP). A numerical computation of the logical whether a copula is left-tail decreasing or right-tail increasing is provided by (isCOP.LTD and isCOP.RTI). The package supports quantile and median regression through (qua.regressCOP, qua.regress2COP, med.regressCOP, med.regress2COP) for a given copula where "2" represents V with respect to U instead of U with respect to V. The regressions can be plotted by (qua.regressCOP.draw).

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Version

Install

install.packages('copBasic')

Monthly Downloads

738

Version

1.5.0

License

GPL

Maintainer

William Asquith

Last Published

September 1st, 2011

Functions in copBasic (1.5.0)

surCOP

The Survival Copula
composite2COP

Composition of Two Copulas
simCOP

Simulate a Copula by Numerical Derivative Method
giniCOP

The Gini's Gamma of a Copula
COP

The Copula
simcomposite3COP

Simulation of a Composited Copula
simcompositeCOP

Simulation of a Composited Copula
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
derCOP

The Numeric Derivative of a Copula
diagCOP

The Diagonals of a Copula
qua.regressCOP

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

Direct Simulation of a Plackett Copula
coCOP

The Co-Copula
lcomoms2.cop2parameter

Convert L-comoments to Parameters of Compositions of Two 2-parameter Copulas
PLACKETTcop

The Plackett Copula
COPinv

The Inverse of a Copula for V with respect to U
rhoCOP

The Spearman's Rho of a Copula
tauCOP

The Kendall's Tau of a Copula
PSP

The ratio of the Product Copula to Summation minus Product Copula
derCOPinv

The Inverse of a Numeric Derivative for V with respect to U of a Copula
P

The Product (Independence) Copula
derCOPinv2

The Inverse of a Numeric Derivative for U with respect to V of a Copula
simCOPmicro

Simulate a V from an U through a Copula by Numerical Derivative Method
duCOP

The Dual of a Copula
W

The Frechet-Hoeffding Lower Bound
N4.2.12cop

The Copula of Equation 4.2.12 of Nelson's Book
sectionCOP

The Sections or Derivative of Sections of a Copula
wolfCOP

The Schweizer and Wolff's Sigma of a Copula
COPinv2

The Inverse of a Copula for U with respect to V
med.regressCOP

Perform Median Regression using a Copula by Numerical Derivative Method for V with respect to U
composite1COP

Composition of a Single Symmetric Copula
composite3COP

Extended Composition of Two Copulas
isCOP.RTI

Is a Copula Right-Tail Increasing
med.regressCOP2

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

The Blomqvist's Beta of a Copula
PlackettPlackettNP

Parameters and L-comoments of a Composition of Two Plackett Copulas
qua.regressCOP2

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

The Frechet-Hoeffding Upper Bound
derCOP2

The Numeric Derivative of a Copula
taildepCOP

The Upper and Lower Tail Dependency Parameters of a Copula
isCOP.LTD

Is a Copula Left-Tail Decreasing
level.curvesCOP

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

Estimate the Parameter of the Plackett Copula