VineCopula (version 2.5.1)

BiCopMetaContour: Contour Plot of Bivariate Meta Distribution

Description

Note: This function is deprecated and only available for backwards compatibility. See contour.BiCop() for contour plots of parametric copulas, and BiCopKDE() for kernel estimates.

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,
  obj = NULL,
  ...
)

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.

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'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'')
16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'')
18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `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)
`104` = Tawn type 1 copula
`114` = rotated Tawn type 1 copula (180 degrees)
`124` = rotated Tawn type 1 copula (90 degrees)
`134` = rotated Tawn type 1 copula (270 degrees)
`204` = Tawn type 2 copula
`214` = rotated Tawn type 2 copula (180 degrees)
`224` = rotated Tawn type 2 copula (90 degrees)
`234` = rotated Tawn type 2 copula (270 degrees)

par

Copula parameter; if empirical contour plot, par = NULL or 0 (default).

par2

Second copula parameter for t-, BB1, BB6, BB7, BB8, Tawn type 1 and type 2 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.

obj

BiCop object containing the family and parameter specification.

...

Additional plot arguments.

Author

Ulf Schepsmeier, Alexander Bauer

See Also

BiCopChiPlot(), BiCopKPlot(), BiCopLambda()

Examples

## meta Clayton distribution  with Gaussian margins
cop <- BiCop(family = 1, tau = 0.5)
BiCopMetaContour(obj = cop, main = "Clayton - normal margins")
# better:
contour(cop, main = "Clayton - normal margins")

## empirical contour plot with standard normal margins
dat <- BiCopSim(1000, cop)
BiCopMetaContour(dat[, 1], dat[, 2], bw = 2, family = "emp",
                 main = "empirical - normal margins")
# better:
BiCopKDE(dat[, 1], dat[, 2],
        main = "empirical - normal margins")

## empirical contour plot with exponential margins
BiCopMetaContour(dat[, 1], dat[, 2], bw = 2,
                 main = "empirical - exponential margins",
                 margins = "exp", margins.par = 1)
# better:
BiCopKDE(dat[, 1], dat[, 2],
         main = "empirical - exponential margins",
         margins = "exp")