EllipticalGenerator {fCopulae} | R Documentation |
A collection and description of functions
concerned with the generator function for
the elliptical copula and with functions
for setting and checking the distributional
parameters.
Functions:
ellipticalList | Returns list of implemented elliptical copulae, |
ellipticalParam | Sets default parameters for an elliptical copula, |
ellipticalRange | returns the range of valid rho values, |
ellipticalCheck | checks if rho is in the valid range, |
| Generator function for elliptical distributions, |
gfuncSlider | Slider for generator, density and probability. |
ellipticalList() ellipticalParam(type = ellipticalList()) ellipticalRange(type = ellipticalList()) ellipticalCheck(rho = 0.75, param = NULL, type = ellipticalList()) gfunc(x, param = NULL, type = ellipticalList()) gfuncSlider(B = 10)
B |
[*Slider] - the maximum slider menu value when the boundary value is infinite. By default this is set to 10. |
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" .
|
x |
[gfunc] - a numeric value or vector out of the range [0,Inf) at
which the generator will be computed.
|
... |
[ellipticalCopulaFit] - arguments passed to the optimization function nlminb .
|
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
.
Diethelm Wuertz for the Rmetrics R-port.
## ellipticalList - # List implemented copulae: ellipticalList() ## gfunc - # Generator Function: gfunc(x = (0:10)/10, param = 2, type = "t") ## gfuncSlider - # Try: if (require(tcltk)) { gfuncSlider() }