Help for package SimCop

Type:

Package

Title:

Simulate from Arbitrary Copulae

Version:

0.7.3

Date:

2025-04-13

Description:

Provides a framework to generating random variates from arbitrary multivariate copulae, while concentrating on (bivariate) extreme value copulae. Particularly useful if the multivariate copulae are not available in closed form. Detailed discussion of the methodologies used can be found in Tajvidi and Turlach (2018) <doi:10.1111/anzs.12209>.

Depends:

R (≥ 4.4.0)

Imports:

grDevices, graphics, quadprog, rgl, stats

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.2

NeedsCompilation:

Packaged:

2025-04-13 10:23:08 UTC; berwin

Author:

Berwin A. Turlach

[aut, cre], Nader Tajvidi

[ctb]

Maintainer:

Berwin A. Turlach <Berwin.Turlach@gmail.com>

Repository:

CRAN

Date/Publication:

2025-04-13 15:50:06 UTC

SimCop: A package to simulate random variates from an arbitrary multivariate copula

Description

R code to support Tajvidi and Turlach (2017). The main functions implemented for the SimCop package are:

New*Copula, various functions that create objects of class ‘SimCop’. These functions return a copula function with various helpful information stored in the environment of the function.

Details of the implementation are subject to change and should not be relied on.

Only a print method is implemented for this class so far.
GetApprox, a function that calculates approximations to a copula and returns an object of class ‘CopApprox’.

For bivariate copulae a method for plot is implemented for this class.
GenerateRV, a generic function that generates random variates from an object, together with a method for objects of class ‘CopApprox’.

Author(s)

Maintainer: Berwin A. Turlach Berwin.Turlach@gmail.com (ORCID)

Other contributors:

Nader Tajvidi Nader.Tajvidi@matstat.lu.se (ORCID) [contributor]

References

Tajvidi, N. and Turlach, B.A. (2017). A general approach to generate random variates for multivariate copulae, Australian & New Zealand Journal of Statistics 60(1): 140–155. doi:10.1111/anzs.12209.

Calculations on cubes

Description

Implements several operations of objects of class ‘ADCube’.

Usage

CrossSum(u, w)

CrossMult(u, w)

CrossDivide(u, w)

CrossSquare(u)

CrossExp(u)

CrossLog(u)

CrossPow(u, r)

CrossSqrt(u)

CrossRaisePow(u, w)

Arguments

u

an object of class ‘ADCube’.

w

an object of class ‘ADCube’.

r

a positive real number.

Details

Assume u and w contain the evaluations of functions f() and g(), together with evaluations of all their cross-derivatives, at points x and y, respectively.

CrossSum returns the evaluation of f()+g(), together with all evaluated cross-derivates.

CrossMult returns the evaluation of f()g(), together with all evaluated cross-derivates.

CrossDivide returns the evaluation of f()/g(), together with all evaluated cross-derivates.

CrossSquare returns the evaluation of (f())^2, together with all evaluated cross-derivates.

CrossExp returns the evaluation of \exp(f()), together with all evaluated cross-derivates.

CrossLog returns the evaluation of \log(f()), together with all evaluated cross-derivates.

CrossPow returns the evaluation of (f())^r, together with all evaluated cross-derivates.

CrossSqrt returns the evaluation of \sqrt{f()}, together with all evaluated cross-derivates.

CrossRaisePow returns the evaluation of f()^{g()}, together with all evaluated cross-derivates.

Value

An object of class ‘ADCube’ is returned. See ‘Details’.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

References

Griewank, A., Lehmann, L., Leovey, H. and Zilberman, M. (2014). Automatic evaluations of cross-derivatives, Mathematics of Computation 83(285): 251-274.

GenerateRV generic

Description

A generic to sample random variates from an object.

Usage

GenerateRV(obj, n, ...)

Arguments

obj

object from which to sample.

n

number of items to sample.

...

further arguments for methods.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Generates random variates from a copula approximation

Description

Method to sample random variates from an object of class ‘CopApprox’.

Usage

## S3 method for class 'CopApprox'
GenerateRV(
  obj,
  n,
  MH = FALSE,
  trace = FALSE,
  PDF = NULL,
  burnin = 500,
  thinning = 5,
  ...
)

Arguments

obj

object from which to sample.

n

number of items to sample.

MH

logical, should a Metropolis-Hastings algorithm be used to refine the sample? Default is FALSE.

trace

logical, indicating whether the function should be verbose.

PDF

probability density function corresponding to copula used to create obj, only used if MH is TRUE; see ‘Details’.

burnin

the number of burn-in iterations of the MH sampler, only used if MH is TRUE, defaults to 500.

thinning

the thining parameter, only used if MH is TRUE, defaults to 5.

...

not used.

Details

If argument MH is FALSE, the default, random variates are directly sampled from the approximation, as described in Tajvidi and Turlach (2017).

If MH is TRUE, GenerateRV uses additionally a Metropolis-Hastings refinement. It first samples from the approximation, but uses those samples then as proposals in a Metropolis-Hastings algorithm. The latter needs the probability density function of the copula. This density function has either to be passed to the argument PDF, or the copula (stored in argument obj) belonging to the approximation must have the density function (with name ‘pdfCopula’) stored in its environment. In the latter case, the argument PDF can be NULL (its default).

Value

A matrix of dimension n times dim, where dim is the dimension for which the copula approximation was determined.

If MH was TRUE the return value has an attribute called ‘AcceptanceRate’, indicating the fraction of samples that were accepted in the Metropolis-Hastings step. This fraction is based on all burnin + (n-1)*thinning + 1 samples that are initially generated from the approximation.

References

Examples

cop <- NewBEVAsyMixedModelCopula(theta=1, phi=-0.25)
approx1 <- GetApprox(cop)
approx2 <- GetApprox(cop, type = 1)
sample1 <- GenerateRV(approx1, 100)
plot(sample1)
sample2 <- GenerateRV(approx2, 100)
plot(sample2)
sample1 <- GenerateRV(approx1, 50, MH = TRUE, trace = TRUE)
plot(sample1)
sample2 <- GenerateRV(approx2, 50, MH = TRUE)
plot(sample2)

Approximate a copula by a histogram density

Description

Approximates the “density” of a copula by a piece-wise constant function.

Usage

GetApprox(
  Cop,
  dim = 2,
  depth = ifelse(type == 1, 10, 32),
  type = 1,
  TOL = 1000 * .Machine$double.eps
)

Arguments

Cop

A function defining the copula.

dim

The approximation should be calculated on the dim-dimensional unit cube, defaults to 2.

depth

The number of hyperrectangles to be used to devide the unit cube, defaults to 10 for Approximation I and to 32 for Approximation II.

type

Whether Approximation I or Approximation II should be used, defaults to one.

TOL

A numerical tolerance used when calculating Approximation I.

Details

This function provides two methods for subdividing the d-dimensional unit cube into hyper-rectangles, with d being passed to the parameter dim. As most of the functions in this package which create a new copula return a function that can be evaluated at points in arbitrary dimensions, it is necessary to specify for which dimension d one wishes to calculate the approximation to the copula's “density”.

The first method (Approximation I) determines 2^m hyper-rectangles (where m is the parameter depth), each containing the same probability mass with respect to the copula. The second method (Approximation II) dividies the unit cube into m^d hyper-squares.

These approximations can be interpreted as piecewise constant approximations of the copula's probability density function if the copula is absolutely continuous. For futher details see ‘References’.

Value

GetApprox returns an object of class ‘CopApprox’ according to its inputs. The returned object is a list containing a matrix that holds the information of the approximation, the argument Cop, which approximation was determined, and other auxiliary information.

The only method for objects of class ‘CopApprox’ implemented so far are for the generic function plot, and then only for the case if dim was 2.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

References

Examples

Cop <- NewMEVGumbelCopula(3)
CopApprox <- GetApprox(Cop, dim=2)
plot(CopApprox)

Extreme temperatures at two West Australian meteorological stations

Description

A dataset on maximum annual values of average daily temperature measurements at two meteorological stations—Leonora (latitude 28.53S, longitude 121.19E) and Menzies (latitude 29.42S, longitude 121.02E)—in Western Australia, for the period 1898–1993.

Usage

MaxTemp

Format

A data frame with 96 rows and 2 variables:

Leonora: annual maximal temperature at Leonora, in degrees Celsius
Menzies: annual maximal temperature at Menzies, in degrees Celsius

References

Hall, P. and Tajvidi, N. (2004). Prediction regions for bivariate extreme events. Australian & New Zealand Journal of Statistics 46(1): 99–112. doi:10.1111/j.1467-842X.2004.00316.x.

Examples

plot(Menzies ~ Leonora, MaxTemp,
     xlab = expression("Temperature at Leonora ("*degree*"C)"),
     ylab = expression("Temperature at Menzies ("*degree*"C)"))

Creates a bivariate asymmetric logistic model extreme value copula

Description

Creates an instance of the bivariate asymmetric logistic model extreme value copula with parameters r, \theta and \phi.

Usage

NewBEVAsyLogisticCopula(r, theta, phi)

Arguments

r

real.

theta

real.

phi

real.

Details

The dependence function for this bivariate EV copula is

A(w) = (\theta (1-w)^r + (\phi w)^r)^{1/r} + (\theta - \phi) w + 1 - \theta

Necessary and sufficient conditions for the dependence function to be valid are

r \ge 1
0 \le \theta \le 0
0 \le \phi \le 1

For \theta = \phi = 1 this model reduces to the symmetric logistic model.

Value

A function that evaluates the bivariate asymmetric logistic model EV copula (with parameters r, \theta and phi) at a given 2-dimensional vector in the unit square. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the bivariate asymmetric mixed model EV copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a bivariate asymmetric mixed model extreme value copula

Description

Creates an instance of the bivariate asymmetric mixed model extreme value copula with parameters \phi and \theta.

Usage

NewBEVAsyMixedModelCopula(theta, phi)

Arguments

theta

real.

phi

real.

Details

The dependence function for this bivariate EV copula is

A(w) = \phi w^3 + \theta w^2 - (\phi+\theta) w + 1

Necessary and sufficient conditions for the dependence function to be valid are

\theta \ge 0
\theta + 3 \phi \ge 0
\theta + \phi \le 1
\theta + 2 \phi \le 1

If \phi = 0 we obtain the symmetric mixed model.

Value

A function that evaluates the bivariate asymmetric mixed model EV copula (with parameters \phi and \theta) at a given 2-dimensional vector in the unit square. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the bivariate asymmetric mixed model EV copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a bivariate logistic model extreme value copula

Description

Creates an instance of the bivariate logistic model extreme value copula with parameter r.

Usage

NewBEVLogisticCopula(r)

Arguments

r

real.

Details

The dependence function for this bivariate EV copula is

A(w) = ((1-w)^r + w^r)^{1/r}

Necessary and sufficient conditions for the dependence function to be valid are

r \ge 1

Value

A function that evaluates the bivariate logistic model EV copula (with parameter r) at a given 2-dimensional vector in the unit square. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the bivariate asymmetric mixed model EV copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a bivariate mixed model extreme value copula

Description

Creates an instance of the bivariate asymmetric mixed model extreme value copula with parameter \theta.

Usage

NewBEVMixedModelCopula(theta)

Arguments

theta

real.

Details

The dependence function for this bivariate EV copula is

A(w) = \theta w^2 - \theta w + 1

Necessary and sufficient conditions for the dependence function to be valid are

0 \le \theta \le 1

Value

A function that evaluates the bivariate asymmetric mixed model EV copula (with parameter \theta) at a given 2-dimensional vector in the unit square. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the bivariate asymmetric mixed model EV copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a flexible extreme value copula

Description

Creates a bivariate extreme value copula from a spline estimate of its dependence function.

Usage

NewBEVSplineCopula(spl)

Arguments

spl

a spline function.

Value

A function that evaluates the bivariate EV copula (whose dependence function is given by the spline) at a given 2-dimensional vector in the unit square. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the bivariate asymmetric mixed model EV copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Cross-derivatives via automatic differentiation

Description

Basic building blocks for evaluating functionals f:R^d \to R and all their cross-derivatives at a given point x \in R^d.

Usage

NewCube(x, j, dim = 2)

Arguments

x

(scalar) value at which the function is evaluated.

j

optional input. See ‘Details’.

dim

dimension d of the input vector, defaults to two.

Details

If the optional argument j is specfied, then the function f(x)=x_j and all its cross-derivatives (all of which but one will be zero, the derivative with respect to the jth component being 1) are evaluated with x_j being set to the value of x.

If the optional argument j is not used, then the function f(x) =c and all its cross-derivatives (all of which will be zero) are evaluated with c beting set to the value of x.

From these primitive function evaluations, more complicated functions can be constructed using the operations documented in CrossSum.

Value

NewCube returns an object of class ‘ADCube’ according to its inputs. See ‘Details’.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

References

Griewank, A., Lehmann, L., Leovey, H. and Zilberman, M. (2014). Automatic evaluations of cross-derivatives, Mathematics of Computation 83(285): 251-274.

Creates a multivariate asymmetric logistic copula

Description

Creates an instance of the multivariate asymmetric copula with parameters \theta and r.

Usage

NewMEVAsyLogisticCopula(theta, r)

Arguments

theta

a k \times d matrix of reals.

r

a vector of k reals

Details

If theta has entries \theta_{ij} and r has entries r_j (i=1,\dots,k and j=1,\dots,d), then the following parameterisation of the copula is used:

C(u_1,\dots,u_d) = \exp\left(- \sum_{i=1}^k \left\{ \sum_{j=1}^d (\theta_{ij} \bar u_j)^{r_i} \right\}^{1/r_i} \right)

where \bar u_j = -\log(u_j), j=1,\dots,d.

Necessary and sufficient conditions for the parameters are

all entries in theta have to be non-negative.
each column of theta has to add to one.
each row of theta must have a unique pattern of non-zero values, including the pattern that has no zeros in a row.
if a row of theta has only one non-zero value, then the corresponding entry in r has to be one.
if a row of theta has more than one non-zero value, then the corresponding entry of r must be greater than one.

Value

A function that evaluates the multivariate asymmetric logistic copula (with parameters \theta and r) at a given d-dimensional vector in the unit square. Note that for this function the dimension of vectors at which the copula can be evaluated is determined by the input parameters. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the multivariate asymmetric logistic copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Examples

theta <-  rbind(c(0, 0.2, 0.8), c(1,0.8,0.2))
r <- c(2,3)
cop <- NewMEVAsyLogisticCopula(theta, r)

## Creates the same copula
theta <- 0.2
phi <- 0.4
r <- 2
cop1 <- NewBEVAsyLogisticCopula(r, theta, phi)
theta <- cbind(c(phi, 1-phi, 0), c(theta, 0, 1-theta))
r <- c(r, 1,  1)
cop2 <- NewMEVAsyLogisticCopula(theta, r)

Creates a Gumpel copula

Description

Creates an instance of the Gumbel copula with parameter r. This family is also known as the Gumbel–Hougaard copula or the logistic model.

Usage

NewMEVGumbelCopula(r = 2)

Arguments

r

real, the parameter of the Gumbel copula, defaults to 2, must be larger or equal to one.

Details

The following parameterisation of the copula is used:

C(u_1,\dots,u_d) = \exp\left(- \left\{ \sum_{j=1}^d \bar u_j^r \right\}^{1/r}\right)

where \bar u_j = -\log(u_j), j=1,\dots,d.

Value

A function that evaluates the Gumbel copula (with parameter r) at a given d-dimensional vector in the unit cube. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the Gumbel copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a Clayton copula

Description

Creates an instance of the Clayton copula with parameter \theta.

Usage

NewMVClaytonCopula(theta = 1)

Arguments

theta

real, the parameter of the Clayton copula, defaults to 1; must be positive.

Details

The following parameterisation of the copula is used:

C(u_1,\dots,u_d) = \left(\left\{ \sum_{j=1}^d u_j^{-\theta} \right\} - (d-1) \right)^{-1/\theta}

Value

A function that evaluates the Clayton copula (with parameter \alpha) at a given d-dimensional vector in the unit cube. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the Clayton copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Creates a Frank copula

Description

Creates an instance of the Frank copula with parameter \alpha.

Usage

NewMVFrankCopula(alpha = 1)

Arguments

alpha

real, the parameter of the Frank copula, defaults to 1; must be positive.

Details

The following parameterisation of the copula is used:

C(u_1,\dots,u_d) = -\log(1+\exp(s) * t)/\alpha

where s = \sum_{j=1}^d \log\left(\frac{\exp(-\alpha u_j) -1 }{t}\right) and t=\exp(-\alpha)-1.

Value

A function that evaluates the Frank copula (with parameter \alpha) at a given d-dimensional vector in the unit cube. The environment of the function also contains a function called pdfCopula that evaluates the probability density function of the Frank copula via automatic differentation.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

Nonparametric estimator of bivariate dependence function

Description

Function to calculate nonparametric estimates of the dependence functions of bivariate extreme value copula.

Usage

NonparEstDepFct(
  x,
  y = NULL,
  w.length = 101,
  transf.to.frechet = TRUE,
  convex.hull = TRUE,
  verbose = FALSE
)

Arguments

x, y

vectors giving the observations of the extreme values. Alternatively a single plotting structure can be specified: see xy.coords.

w.length

number of grid points (using an equidistant grid from 0 to 1) on which the dependence function is estimated.

transf.to.frechet

logical, controls whether x and y are first transformed to have standard Fréchet margins: see ‘Details’; defaults to TRUE.

convex.hull

logical, controls whether the convex hull of the modified Pickands estimator is returned; defaults to TRUE.

verbose

logical, controls whether progress messages are given; defaults to FALSE.

Details

If transf.to.frechet is TRUE, the default, then a generalised extreme value (GEV) distribution is fitted to each margin and the fitted parameters are used to transform the data to have standard Fréchet margins. The parameterisation of the cumulative distribution of the GEV that is used is, if \gamma \neq 0:

G(z) = \exp\left(-\left[1+\gamma\left(\frac{z-\mu}{\sigma}\right)\right]^{-1/\gamma}\right)

and for \gamma = 0:

G(z) = \exp(-\exp(-z))

If \gamma < 0, then the support of the GEV is the interval (-\infty, \mu - \sigma/\gamma], while it is [\mu - \sigma/\gamma, \infty) if \gamma > 0. For \gamma = 0, the support is the real line.

If verbose is TRUE, not the default, and transf.to.frechet is TRUE, the estimates for the fitted GEV distribution are printed out using cat.

Value

A list with two named components. The component x contains a vector with the grid points at which the dependence function was estimated. The component y contains the estimated dependence functions.

Author(s)

Nader Tajvidi Nader.Tajvidi@matstat.lu.se

References

Hall, P. and Tajvidi, N. (2000). Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 6(5): 835–844. doi:10.2307/3318758.

Hall, P. and Tajvidi, N. (2004). Prediction regions for bivariate extreme events. Australian & New Zealand Journal of Statistics 46(1): 99–112. doi:10.1111/j.1467-842X.2004.00316.x.

Examples

## Data from Hall and Tajvidi (2004, ANZJS)
EstDF1 <- NonparEstDepFct(MaxTemp)

## Plot modified Pickands Function and area in which
## dependence function must lie
plot(EstDF1, ylim = c(0.5,1), xlab = "w", ylab = "A(w)", type="l", lty="longdash")
polygon(c(0, 0.5, 1, 0), c(1, 0.5, 1, 1))

Fit a dependence function by spline smoothing

Description

Given estimates for the dependence function of a bivariate extreme value copula at specified points, this function fits a natural cubic smoothing spline, that is constrained to fulfill all the conditions of a dependence function, to the given estimates via quadratic programming.

Usage

SplineFitDepFct(x, y = NULL, alpha = 0.01, integ.value)

Arguments

x, y

vectors giving the coordinates of the points to be approximated. Alternatively a single plotting structure can be specified: see xy.coords.

alpha

real, the smoothing parameter for the smoothing splines.

integ.value

real, non-negative value that should be less than two; see ‘Details’

Details

integ.value should be between 0 and 2. If a value is specified, then an additional constraint is added to the quadratic program to ensure that the integeral (over 0 to 1) of the second derivative of the spline is larger or equal to integ.value. Choosing values close to 2 may lead to quadratic programms on which solve.QP reports inconsistent constraints.

Value

A function, created by splinefun, that evaluates the natural cubic spline that was fitted to the data.

Author(s)

Nader Tajvidi Nader.Tajvidi@matstat.lu.se

Berwin A Turlach Berwin.Turlach@gmail.com

References

Hall, P. and Tajvidi, N. (2000). Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 6(5): 835–844. doi:10.2307/3318758.

Hall, P. and Tajvidi, N. (2004). Prediction regions for bivariate extreme events. Australian & New Zealand Journal of Statistics 46(1): 99–112. doi:10.1111/j.1467-842X.2004.00316.x.

Examples

## Data from Hall and Tajvidi (2004, ANZJS)
EstDF2 <- NonparEstDepFct(MaxTemp, convex = FALSE)

## Plot modified Pickands Function and area in which
## dependence function must lie
plot(EstDF2, ylim = c(0.5,1), xlab = "w", ylab = "A(w)", type="l", lty="longdash")
polygon(c(0, 0.5, 1, 0), c(1, 0.5, 1, 1))

## Fit spline to Pickands function and add to plot
splfit <- SplineFitDepFct(EstDF2)
curve(splfit, n = 301, add = TRUE, lty = "dashed")

Plot the histogram density approximation to a copula

Description

Plots the histogram density approximation to a copula as determined by GetApprox. Currently works only for bivariate copulae.

Usage

## S3 method for class 'CopApprox'
plot(
  x,
  type = c("rgl", "original"),
  col = if (type == "rgl") "#cccccc" else grey.colors(100, start = 0, end = 0.8),
  qcut = 0.95,
  cut,
  alpha = 1,
  topcol = "#ff0000",
  sidecol = "#aaaaaa",
  linecol = "#000000",
  ...
)

Arguments

x

an object of class ‘CopApprox’.

type

specifies the type of plot to produce. Possible values are “rgl” and “original”; see ‘Details’. Can be abbreviated.

col

colour(s) to be used; see ‘Details’.

qcut, cut

used if type is “rgl”; see ‘Details’.

alpha, topcol, sidecol, linecol

used if type is “rgl”; see ‘Details’.

...

used if type is “original”; see ‘Details’.

Details

If type is “original” then plots are produced of the kind shown in Tajvidi and Turlach (2017). In this case the dot arguments are passed to plot when the initial plot is created. Thus, they can be used to set the main title, axes labels and so forth. If the approximation is of type Approximation II, then argument col is used to colour the squares while they are plotted and filled via polygon. For this, the ranks of the probability masses of the squares are mapped (linearly) onto the provided colours.

If type is “rgl” then plots are used using rgl. The code used is based on the ‘hist3d’ demo of the rgl package. The argument col sets the background colour of the plot. Arguments topcol and sidecol are used to set the colour of the top and sides of the cuboids, and the edges of the cuboids are drawn using linecol. Argument alpha sets the transparency. Finally, as the heights of the cuboids can be large, in particular for extreme value copulae, their heights are truncated using either cut (absolute value) or qcut (corresponding quantile of all heights as determined by the quantile function). After truncation, the heights are rescaled to be between 0 and 1, thus the unit on the “z”-axis is meaningless.

Value

NULL is returned invisibly.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

References

Examples

Cop <- NewMEVGumbelCopula(4)
CopApprox1 <- GetApprox(Cop, dim=2)
plot(CopApprox1)
plot(CopApprox1, type = "o")
CopApprox2 <- GetApprox(Cop, dim=2, type=2)
plot(CopApprox2)
plot(CopApprox2, type = "o", xlab = expression(u[1]), ylab = expression(u[2]))
plot(CopApprox2, type = "o", col = heat.colors(100))

Plot a bivariate copula or its density

Description

Plot a bivariate copula or its density function. Essentially hands over immediately to persp3d.

Usage

## S3 method for class 'SimCop'
plot(x, ...)

## S3 method for class 'SimCop'
persp3d(
  x,
  ...,
  type = c("cdf", "pdf"),
  nx = 129,
  ny = 129,
  col = heat.colors(100),
  qcut = 0.95,
  cut,
  xlab = expression(u[1]),
  ylab = expression(u[2])
)

Arguments

x

an object of class ‘SimCop’.

...

additional arguments passed to persp3d.

type

specifies whether the copula (“cdf”) or its probability density function (“pdf”) is plotted; see ‘Details’. Can be abbreviated.

nx, ny

length of grids that define the gridlines on which the plotted function is evaluated.

col

colour scheme to use for the surface; see ‘Details’.

qcut, cut

used if type is “pdf”; see ‘Details’.

xlab, ylab

default labels for the two axes.

Details

If type is “pdf”, then x must have a function with name “pdfCopula” in its environment which evaluates the probability density function of the copula stored in x.

For plotting the copula, the “x”-grid and “y”-grid are produced by using, respectively, nx and ny equispaced points between 0 and 1 (inclusive). To avoid evaluating the density function at the boundary, if type is “pdf”, then grids are initially generated in the same manner, after which the first grid point is removed and all remaining grid points are shifted towards the origin by half the distance between two neighbouring grid points.

The function to be plotted is evaluated at all possible combination of the grid points. As the function values of the density function can be large, in particular for extreme value copulae, the values are truncated using either cut (absolute value) or qcut (corresponding quantile of all values as determined by the quantile function).

Finally, the colour scheme passed by argument col is used to assign a colour to every point at which the function was evaluated by linearly mapping the function values onto the provided colours.

Value

Returns a list with four components invisibly. Components x and y contain the location of grid lines at which the function was evaluate. Component z contains the function evaluations (possibly truncated) and component col contains the col used.

Author(s)

Berwin A Turlach berwin.turlach@gmail.com

Examples

Cop1 <- NewMVFrankCopula(2)
plot(Cop1)
plot(Cop1, type = "p", qcut = 1)

Print method for cubes

Description

print method for ‘ADCube’ objects.

Usage

## S3 method for class 'ADCube'
print(x, ...)

Arguments

x

an object of class ‘ADCube’.

...

arguments passed on to base::print.

Details

Currently, the component ‘val’ of the ‘ADCube’ object is printed using base::print.

Print basic information on a copula

Description

Prints basic information on a copula created with the methods in this package.

Usage

## S3 method for class 'SimCop'
print(x, ...)

Arguments

x

an object of class ‘SimCop’.

...

not used.

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com

SimCop: A package to simulate random variates from an arbitrary multivariate copula

Description

Author(s)

References

Calculations on cubes

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

GenerateRV generic

Description

Usage

Arguments

Author(s)

Generates random variates from a copula approximation

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Approximate a copula by a histogram density

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Extreme temperatures at two West Australian meteorological stations

Description

Usage

Format

References

Examples

Creates a bivariate asymmetric logistic model extreme value copula

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Creates a bivariate asymmetric mixed model extreme value copula

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Creates a bivariate logistic model extreme value copula

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Creates a bivariate mixed model extreme value copula

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Creates a flexible extreme value copula

Description

Usage

Arguments

Value