# BiCopMetaContour: Contour plot of bivariate meta distribution with different... In CDVine: Statistical Inference of C- And D-Vine Copulas

## 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

 ```1 2 3 4``` ```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

`BiCopChiPlot`, `BiCopKPlot`, `BiCopLambda`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```## 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) ```