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rmixture-model

R: Calculating the probability density function of a special definition of Skew-T Distribution

I currently work with the mixture model package EMMIXskew and I have fitted a skew-t Distribution on my data (some numerical vector). The package has some density function ddmst but I haven't seen a probability density function in this package and I need some!

What I thought I could do is

  1. use some other packages which provides a pdf for skew-t distribution, like package sn with pst, but the problem is that this distribution has a different definition of skew-t distribution, OR
  2. I could use integrate on ddmst, but it doesn't work so far.

I tried something like

library(EMMIXskew)

dat <- rdmst(n=1000,p=1,mean=0,cov=1,del=1)

mu=0.01
sigma=0.9
nu=1.1
del=3
pdmst <- function(x){     
  ddmst(x,n=length(dat),p=1,mean=mu,cov=sigma,nu=nu,del=del)
}

x=0.6

F_x <- integrate(pdmst,lower=-Inf,upper=x)

and also if I assume 3-modality of my data with parameters

mu=c(0.01,2,-0.4)
sigma=c(0.9,2,2.3)
nu=c(1.1,1,0.8)
del=c(3,2,1.2)
pdmst <- function(x){     
  ddmst(x,n=length(dat),p=1,mean=mu,cov=sigma,nu=nu,del=del)

I get this error

Error in ddmix(dat, n, p, 1, "mst", mean, cov, nu, del) : dat does not match n and p.

I really don't know what I did wrong!

Solution

  • Try this:

    pdmst <- function(x){    
  ddmst(x,n=length(x),p=1,mean=mu,cov=sigma,nu=nu,del=del)
}

    n should be the length of x instead of dat. Then pdmst(x) should give you the density at x.

    For the 3-component case, please refer to the documentation of ddmix on how to specify the arguments of this function. For your second example, it can be entered as follows:

    mu = cbind(0.01, 2, -0.4)
sigma = cbind(0.9,2,2.3)
del = cbind(3,2,1.2)
nu=c(1.1,1,0.8)
ddmix(x,1,1,3,"mst",mu, sigma, nu, del)

    The final command should give you the logarithm of the density at x for each of the three components.