BiCopMetaContour {CDVine} | R Documentation |
Contour plot of bivariate meta distribution with different margins and copula (theoretical and empirical)
Description
This function plots a bivariate contour plot corresponding to a bivariate meta distribution with different margins
and specified bivariate copula and parameter values or creates corresponding empirical contour plots based on bivariate copula data.
Usage
BiCopMetaContour(u1=NULL, u2=NULL, bw=1, size=100,
levels=c(0.01,0.05,0.1,0.15,0.2),
family="emp", par=0, par2=0, PLOT=TRUE,
margins="norm", margins.par=0, xylim=NA, ...)
Arguments
u1,u2 |
Data vectors of equal length with values in [0,1] (default: u1 and u2 = NULL ).
|
bw |
Bandwidth (smoothing factor; default: bw = 1 ).
|
size |
Number of grid points; default: size = 100 .
|
levels |
Vector of contour levels.
For Gaussian, Student t or exponential margins the default value (levels = c(0.01,0.05,0.1,0.15,0.2) ) typically is a good choice.
For uniform margins we recommend
levels = c(0.1,0.3,0.5,0.7,0.9,1.1,1.3,1.5)
and for Gamma margins
levels = c(0.005,0.01,0.03,0.05,0.07,0.09) .
|
family |
An integer defining the bivariate copula family or indicating an empirical contour plot:
"emp" = empirical contour plot (default; margins can be specified by margins )
0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
7 = BB1 copula
8 = BB6 copula
9 = BB7 copula
10 = BB8 copula
13 = rotated Clayton copula (180 degrees; “survival Clayton”)
14 = rotated Gumbel copula (180 degrees; “survival Gumbel”)
16 = rotated Joe copula (180 degrees; “survival Joe”)
17 = rotated BB1 copula (180 degrees; “survival BB1”)
18 = rotated BB6 copula (180 degrees; “survival BB6”)
19 = rotated BB7 copula (180 degrees; “survival BB7”)
20 = rotated BB8 copula (180 degrees; “survival BB8”)
23 = rotated Clayton copula (90 degrees)
24 = rotated Gumbel copula (90 degrees)
26 = rotated Joe copula (90 degrees)
27 = rotated BB1 copula (90 degrees)
28 = rotated BB6 copula (90 degrees)
29 = rotated BB7 copula (90 degrees)
30 = rotated BB8 copula (90 degrees)
33 = rotated Clayton copula (270 degrees)
34 = rotated Gumbel copula (270 degrees)
36 = rotated Joe copula (270 degrees)
37 = rotated BB1 copula (270 degrees)
38 = rotated BB6 copula (270 degrees)
39 = rotated BB7 copula (270 degrees)
40 = rotated BB8 copula (270 degrees)
|
par |
Copula parameter; if empirical contour plot, par = NULL or 0 (default).
|
par2 |
Second copula parameter for t-, BB1, BB6, BB7 and BB8 copulas (default: par2 = 0 ).
|
PLOT |
Logical; whether the results are plotted.
If PLOT = FALSE , the values x , y and z are returned (see below; default: PLOT = TRUE ).
|
margins |
Character; margins for the bivariate copula contour plot. Possible margins are:
"norm" = standard normal margins (default)
"t" = Student t margins with degrees of freedom as specified by margins.par
"gamma" = Gamma margins with shape and scale as specified by margins.par
"exp" = Exponential margins with rate as specified by margins.par
"unif" = uniform margins
|
margins.par |
Parameter(s) of the distribution of the margins if necessary (default: margins.par = 0 ), i.e.,
a positive real number for the degrees of freedom of Student t margins (see dt ),
a 2-dimensional vector of positive real numbers for the shape and scale parameters of Gamma margins (see dgamma ),
a positive real number for the rate parameter of exponential margins (see dexp ).
|
xylim |
A 2-dimensional vector of the x- and y-limits.
By default (xylim = NA ) standard limits for the selected margins are used.
|
... |
Additional plot arguments.
|
Value
x |
A vector of length size with the x-values of the kernel density estimator with Gaussian kernel
if the empirical contour plot is chosen and a sequence of values in xylim if the theoretical contour plot is chosen.
|
y |
A vector of length size with the y-values of the kernel density estimator with Gaussian kernel
if the empirical contour plot is chosen and a sequence of values in xylim if the theoretical contour plot is chosen.
|
z |
A matrix of dimension size with the values of the density of the meta distribution
with chosen margins (see margins and margins.par ) evaluated at the grid points given by x and y .
|
Note
Warning: The combination family = 0
(independence copula) and margins = "unif"
(uniform margins) is not possible because all z
-values are equal.
Author(s)
Ulf Schepsmeier, Alexander Bauer
See Also
BiCopChiPlot
, BiCopKPlot
, BiCopLambda
Examples
## Example 1: contour plot of meta Gaussian copula distribution
## with Gaussian margins
tau = 0.5
fam = 1
theta = BiCopTau2Par(fam,tau)
BiCopMetaContour(u1=NULL,u2=NULL,bw=1,size=100,
levels=c(0.01,0.05,0.1,0.15,0.2),
family=fam,par=theta,main="tau=0.5")
## Example 2: empirical contour plot with standard normal margins
dat = BiCopSim(N=1000,fam,theta)
BiCopMetaContour(dat[,1],dat[,2],bw=2,size=100,
levels=c(0.01,0.05,0.1,0.15,0.2),
par=0,family="emp",main="N=1000")
# empirical contour plot with exponential margins
BiCopMetaContour(dat[,1],dat[,2],bw=2,size=100,
levels=c(0.01,0.05,0.1,0.15,0.2),
par=0,family="emp",main="n=500",
margins="exp",margins.par=1)
[Package
CDVine version 1.4
Index]