sn (version 0.4-18)

dst2.plot: Plot of bivariate skew-$t$ density function

Description

Produces a contour plot of the density function of a bivariate skew-$t$ variate.

Usage

dst2.plot(x, y, xi, Omega, alpha, df, dp = NULL, ...)

Arguments

x

vector of values of the first component.

y

vector of values of the second component.

xi

a vector of length 2 containing the location parameter.

Omega

a 2 by 2 matrix containing a covariance matrix.

alpha

a vector of length 2 containing the shape parameter.

df

a positive number, representing the degrees of freedom .

dp

a list with components named xi, Omega, alpha, df, containing quantities as described above. If this parameter is set, then the individual parameters must not be.

...

additional parameters to be passed to contour.

Value

• A list containing the original input parameters plus a matrix containing the density function evaluated at the grid formed by the x and y values.

Background

The family of multivariate skew-t distributions is an extension of the multivariate Student's $t$ family, via the introduction of a shape parameter which regulates skewness; when shape=0, the skew-$t$ distribution reduces to the usual $t$ distribution. When df=Inf the distribution reduces to the multivariate skew-normal one; see dmsn. See the reference below for additional information.

Details

Typical usages are dst2.plot(x, y, xi, Omega, alpha, df, ...) dst2.plot(x, y, dp=, ...) The density function is evalutate at the grid of points whose coordinates are given by vectors x and y. The actual computation is done by the function dmst. A contour level plot is produced on the graphical window.

References

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution. J.Roy. Statist. Soc. B 65, 367--389.

See Also

dmst, dsn2.plot

Examples

x <- y <- seq(-5, 5, length=35)
dst2.plot(x, y, c(-1,2), diag(c(1,2.5)), c(2,-3), df=5)