EllipticalCopulae {fCopulae} | R Documentation |
Bivariate Elliptical Copulae
Description
A collection and description of functions to investigate bivariate elliptical copulae.Elliptical Copulae Functions:
rellipticalCopula | Generates elliptical copula variates, |
pellipticalCopula | computes elliptical copula probability, |
dellipticalCopula | computes elliptical copula density, |
rellipticalSlider | displays interactive plots of variates, |
pellipticalSlider | displays interactive plots of probability, |
dellipticalSlider | displays interactive plots of density. |
Usage
rellipticalCopula(n, rho = 0.75, param = NULL, type = c("norm", "cauchy", "t")) pellipticalCopula(u = 0.5, v = u, rho = 0.75, param = NULL, type = ellipticalList(), output = c("vector", "list"), border = TRUE) dellipticalCopula(u = 0.5, v = u, rho = 0.75, param = NULL, type = ellipticalList(), output = c("vector", "list"), border = TRUE) rellipticalSlider(B = 100) pellipticalSlider(type = c("persp", "contour"), B = 20) dellipticalSlider(type = c("persp", "contour"), B = 20)
Arguments
B |
[*Slider] - the maximum slider menu value when the boundary value is infinite. By default this is set to 10. |
border |
[pellipticalCopula][dellipticalCopula] - a logical flag. If the argument u is an integer, say N ,
greater than one than all points on a square grid [(0:N)/N]^2
are computed. If border is FALSE than the border points are removed
from the returned value, by default this is not the case.
|
n |
[rellipticalCopula][ellipticalCopulaSim] - the number of random deviates to be generated, an integer value. |
output |
[pellipticalCopula][dellipticalCopula] - a character string specifying how the output should be formatted. By default a vector of the same length as u and v
is returned. If specified as "list" then u and v
are expected to span a two-dimensional grid as outputted by the
function grid2d and the function returns a list with
elements $x , y , and z which can be directly
used for example by 2D plotting functions. For the grid version,
when u is specified as an integer greater than one, always
the output in form of a list will be returned.
|
rho |
[*ellipticalCopula] - is the numeric value setting the correlation strength, ranging between minus one and one. |
param |
[*ellipticalCopula][gfunc] - additional distributional parameters: for the Sudent-t distribution this is "nu", for the Kotz distribution this is "r", and for the Exponential Power distribution these are "r" and "s". If the argument param=NULL then default values are taken. These are
for the Student-t param=c(nu=4)) , for the Kotz distribution
param=c(r=1)) , and for the exponential power distribution
param=c(r=1,s=1) . Note, that the Kotz and exponential power
copulae are independent of r , and that r only enters
the generator, the density, the probability and the quantile
functions.
|
type |
[*ellipticalCopula][gfunc] - the type of the elliptical copula. A character string selected from: "norm", "cauchy", "t", "logistic", "laplace", "kotz", or "epower". [*ellipticalSlider] - a character string which indicates what kind of plot should be displayed, either a perspective plot if type="persp" , the
default value, or a contour plot if type="contour" .
|
u, v |
[*ellipticalCopula] - two numeric values or vectors of the same length at which the copula will be computed. If u is a list then the
the $x and $y elements will be used as u
and v . If u is a two column matrix then the
first column will be used as u and the the second
as v . If u is an integer value greater than one,
say N , than the values for all points on the
[(0:N)/N]^2 grid spanning the unit square will be returned.
|
... |
[ellipticalCopulaFit] - arguments passed to the optimization function nlminb .
|
Value
Copula Functions:The functions
[rpd]ellipticalCopula
return a numeric vector
of random variates, probabilities, or densities for the specified
copula computed at grid coordinates u
|v
.
The functions
[rpd]ellipticalSlider
display an interactive
graph of an perspective copula plot either for random variates,
probabilities or densities. Alternatively, an image underlayed
contour plot can be shown.
Copula Dependence Measures:
The functions
ellipticalTau
and ellipticalRho
return
a numericc value for Kendall's Tau and Spearman's Rho.
Copula Tail Coefficient:
The function
ellipticalTailCoeff
returns the coefficient of
tail dependence for a specified copula. The function
ellipticalTailPlot
displays a whole plot for the upper or
alternatively for the lower tail dependence as a function of
u
for a set of nine rho
values.
Copula Generator Function:
The function
gfunc
computes the generator function for the
specified copula, by default the normal copula. If the argument
x
is missing, then the normalization constand lambda will
be returned, otherwise if x
is specified the values for the
function g(x) will be freturned. The selected type of copula
is added to the output as an attribute named "control"
.
The function gfuncSlider
allows to display interactively
the generator function, the marginal density, the marginal
probability, and the contours of the the bivariate density.
Copula Simulation and Parameter Fitting:
The function
ellipticalCopulaSim
returns a numeric two-column
matrix with randomly generated variates for the specified copula.
The function
ellipticalCopulaFit
returns a fit to empirical
data for the specified copula. The returned object is a list with
elements from the function nlminb
.
Author(s)
Diethelm Wuertz for the Rmetrics R-port.Examples
## [rp]ellipticalCopula - # Default Normal Copula: rellipticalCopula(10) pellipticalCopula(10) ## [rp]ellipticalCopula - # Student-t Copula Probability and Density: u = grid2d(x = (0:25)/25) pellipticalCopula(u, rho = 0.75, param = 4, type = "t", output = "list") d = dellipticalCopula(u, rho = 0.75, param = 4, type = "t", output = "list") persp(d, theta = -40, phi = 30, col = "steelblue") ## ellipticalTau - ## ellipticalRho - # Dependence Measures: ellipticalTau(rho = -0.5) ellipticalRho(rho = 0.75, type = "logistic", subdivisions = 100) ## ellipticalTailCoeff - # Student-t Tail Coefficient: ellipticalTailCoeff(rho = 0.25, param = 3, type = "t") ## gfunc - # Generator Function: plot(gfunc(x = 0:10), main = "Generator Function") ## ellipticalCopulaSim - ## ellipticalCopulaSim - # Simualtion and Parameter Fitting: rv = ellipticalCopulaSim(n = 100, rho = 0.75) ellipticalCopulaFit(rv)
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