CODEWITHSUNDEEP
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user2005253
user2005253

Reputation:

Generating random variables from the multivariate t-distribution

I wanted to generate random variables from a multivariate t distribution in R. i am using the mvtnorm package which has the command rmvt for generating random variables from the multivariate t-distribution. Now my question is about the syntax of the function and being able to manipulate it to do what I want. The function requires the following 

rmvt(n, sigma = diag(2), df = 1, delta = rep(0, nrow(sigma)),
     type = c("shifted", "Kshirsagar"), ...)

where sigma is a correlation matrix. Now what I am having trouble with is how to sample from a multivariate t-distribution with mean m and covariance matrix S. Is the following the appropriate syntax?

rmvt(1,S,df=n) + m

or 

rmvt(1,R,df=n)*sigma + m

where my covariance matrix can be decomposed as S = sigma*R (i.e., R is my correlation matrix). I am getting different results when I run the two lines of code so that is partially where my confusion stems from.

Upvotes: 2

Views: 5129

Answers (1)

Macro
Macro

Reputation: 1510

Have a look at the help file for rmvt. There is says that sigma is the scale (not correlation) matrix and that the correlation matrix, which is only defined for df>2 is given by sigma * df/(df-2). Therefore is you have a pre-specified covariance matrix S then you should set 

sigma=S*(D-2)/D

where D is the degrees of freedom. To generate n samples from the multivariate t-distribution with mean m and covariance matrix S you can either add the mean outside the call to rmvt, as you indicated: 

rmvt(n, sigma=S*(D-2)/D, df=D) + m

or by using the mu argument:

rmvt(n, mu=m, sigma=S*(D-2)/D, df=D)

Edit: For whatever reason, rmvt is not loading properly on my machine so I have to type this first to have the function loaded properly: 

rmvt <- bfp:::rmvt

Upvotes: 4

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