Contour Plot of Bivariate Meta Distribution

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.

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,
  ...
)

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.

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

The combination family = 0 (independence copula) and margins = "unif" (uniform margins) is not possible because all z-values are equal.

Author

Ulf Schepsmeier, Alexander Bauer

Examples

## meta Clayton distribution  with Gaussian margins
cop <- BiCop(family = 1, tau = 0.5)
BiCopMetaContour(obj = cop, main = "Clayton - normal margins")
#> Warning: This function is deprecated. See ?contour.BiCop for contour plots of parametric copulas
#>   and ?BiCopKDE for kernel estimates.

# 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")
#> Warning: This function is deprecated. See ?contour.BiCop for contour plots of parametric copulas
#>   and ?BiCopKDE for kernel estimates.

# better:
BiCopKDE(dat[, 1], dat[, 2],
        main = "empirical - normal margins")
#> Error in BiCopKDE(dat[, 1], dat[, 2], main = "empirical - normal margins"): The 'kdecopula' package must be installed.

## empirical contour plot with exponential margins
BiCopMetaContour(dat[, 1], dat[, 2], bw = 2,
                 main = "empirical - exponential margins",
                 margins = "exp", margins.par = 1)
#> Warning: This function is deprecated. See ?contour.BiCop for contour plots of parametric copulas
#>   and ?BiCopKDE for kernel estimates.

# better:
BiCopKDE(dat[, 1], dat[, 2],
         main = "empirical - exponential margins",
         margins = "exp")
#> Error in BiCopKDE(dat[, 1], dat[, 2], main = "empirical - exponential margins",     margins = "exp"): The 'kdecopula' package must be installed.

Arguments

Value

Note

See also

Author

Examples