Description Usage Arguments Details Value References Examples
dskewt
gives the multivariate skew-t density,
dmixskewt
for a mixture of multivariate skew-t densities.
rskewt
draws random values from the multivariate skew-t density,
rmixskewt
from a mixture of multiviariate skew-t's.
1 2 3 4 5 6 7 |
x |
Vector, matrix or data.frame with values at which to evaluate the density |
n |
Number of random draws to be obtained |
mu |
For dskewt and rskewt mu is a vector indicating the location parameter. For dmixskewt and rmixskewt mu is a list of location parameters for each component |
Sigma |
For dskewt and rskewt Sigma is the scale matrix. For dmixskewt and rmixskewt it is a list of scale matrices for each component |
A |
Optional matrix containing eigenvectores of Sigma, i.e. Sigma= t(A) D A. For identifiability all elements in A[,1] must be positive, if any entry is negative then the corresponding row is changed sign |
D |
Optional diagonal matrix with eigenvalues of Sigma, i.e. Sigma= t(A) D A. For identifiability these are assumed to be in decreasing order. |
alpha |
For dskewt and rskewt alpha is the vector or asymmetry parameters. For dmixskewt and rmixskewt it is a list of asymmetry parameters for each component |
nu |
For |
probs |
Vector with mixture component weights |
param |
Set to 'eps' for the epsilon-skew parametization, 'isf' for the inverse scale factor parameterization. See help(dtp3) for details |
ttype |
Set to 'independent' for iskew-t, to 'dependent' for dskew-t |
logscale |
If set to |
A draw from the iskew-t distribution is obtained as y= sqrt(D) A x, where x is a vector with independent draws from univariate t distributions.
A draw from the dskew-t distribution is obtained as y= sqrt(D) A x, where x is a draw from a multivariate t distribution with identity scale matrix. That is, the elements in x are dependent but uncorrelated, in constrast with the iskew-t where they are independent.
dskewt
and dmixskewt
return a vector with the probability density
function evaluated at the given x
.
rskewt
and rmixskewt
return a matrix with the generated random draws.
Rossell D., Steel M.F.J. Continuous non-Gassian mixtures. In Handbook of Cluster Analysis, CRC Press.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | #Single skew-t
library(twopiece)
n <- 100; mu1 <- c(0,0); S1 <- matrix(c(1,0,0,1),nrow=2)
alpha1 <- c(0,0); nu1 <- 100
y1 <- rskewt(n,mu=mu1,Sigma=S1,alpha=alpha1,nu=nu1,param='eps')
xseq <- seq(-3,3,length=10)
xgrid <- expand.grid(xseq,xseq)
dy1 <- dskewt(xgrid,mu=mu1,Sigma=S1,alpha=alpha1,nu=nu1)
#Mixture of skew-t's
n <- 100; probs <- c(2/3,1/3); param <- 'eps'
mu1 <- c(0,0); S1 <- matrix(c(1,0,0,1),nrow=2)
alpha1 <- c(0,0); nu1 <- 100
mu2 <- c(3,3); S2 <- matrix(c(1,.5,.5,1),nrow=2)
alpha2 <- c(-.5,0); nu2 <- 100
mu <- list(mu1,mu2); Sigma <- list(S1,S2); alpha <- list(alpha1,alpha2); nu <- list(nu1,nu2)
xsim <- rmixskewt(n,mu=mu,Sigma=Sigma,alpha=alpha,nu=nu,probs=probs,param=param)
head(xsim$x) #simulated values
head(xsim$cluster) #true cluster
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