dmst {sn} | R Documentation |
Probability density function, distribution function and random number generation for the multivariate skew-t (MST) distribution.
dmst(x, xi=rep(0,length(alpha)), Omega, alpha, df=Inf, log=FALSE) dmst(x, dp=, log=FALSE) pmst(x, xi=rep(0,length(alpha)), Omega, alpha, df=Inf, ...) pmst(x, dp=, ...) rmst(n=1, xi=rep(0,length(alpha)), Omega, alpha, df=Inf) rmst(n=1, dp=)
x |
for dmsn , this is either a vector of length d ,
where d=length(alpha) , or a matrix with d columns,
giving the coordinates of the point(s) where the density must be
avaluated; for pmsn , only a vector of length d is allowed.
|
xi |
a numeric vector of lenght d , or a matrix with d columns,
representing the location parameter of the distribution.
If xi is a matrix, its dimensions must agree with those of x .
|
Omega |
a positive-definite covariance matrix of dimension (d,d) .
|
alpha |
a numeric vector which regulates the shape of the density. |
df |
degrees of freedom (scalar); default is df=Inf which corresponds
to the multivariate skew-normal distribution.
|
dp |
a list with three elements named xi , Omega , alpha
and df , containing quantities as described above.
If dp is specified, this overrides the individual parameter
specification.
|
n |
a numeric value which represents the number of random vectors to be drawn. |
log |
logical; if TRUE, densities are given as log-densities. |
... |
additional parameters passed to pmt
|
The positive-definiteness of Omega
is not tested for
efficiency reasons. Function
pmst
requires pmt
from package mnormt
;
the accuracy of its computation can be controlled via use of ...
A vector of density values (dmst
) or a single probability
(pmst
) or a matrix of random points (rmst
).
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.
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.
x <- seq(-4,4,length=15) xi <- c(0.5, -1) Omega <- diag(2) Omega[2,1] <- Omega[1,2] <- 0.5 alpha <- c(2,2) pdf <- dmst(cbind(x,2*x-1), xi, Omega, alpha, df=5) rnd <- rmst(10, xi, Omega, alpha, 6) p1 <- pmst(c(2,1), xi, Omega, alpha, df=5) p2 <- pmst(c(2,1), xi, Omega, alpha, df=5, abseps=1e-12, maxpts=10000)