# [R] Generating samples from truncated multivariate Student-t distribution

peter dalgaard pdalgd at gmail.com
Wed May 10 21:09:30 CEST 2017

```It's not obvious to me that that marginal distribution of one component of a multivariate truncated t is the corresponding univariate truncated t.

In fact, I would expect it to differ because of tail-dependence effects, e.g.

> r <- rtmvt(1e5, c(30,0), diag(2), lower=c(29,-Inf), upper=c(31, +Inf), df=4)
> sd(r[,2])
[1] 1.191654
> r <- rtmvt(1e5, c(30,0), diag(2), lower=c(35,-Inf), upper=c(37, +Inf), df=4)
> sd(r[,2])
[1] 3.504233

-pd

> On 9 May 2017, at 19:09 , Czarek Kowalski <czarek230800 at gmail.com> wrote:
>
> Dear Members,
> I am working with 6-dimensional Student-t distribution with 4 degrees
> of freedom truncated to [20; 60]. I have generated 100 000 samples
> from truncated multivariate Student-t distribution using rtmvt
> function from package ‘tmvtnorm’. I have also calculated  mean vector
> using equation (3) from attached pdf. The problem is, that after
> summing all elements in one column of rtmvt result (and dividing by
> 100 000) I do not receive the same result as using (3) equation. Could
> You tell me, what is incorrect, why there is a difference?
> Yours faithfully
> Czarek Kowalski
> <truncatedT.pdf>______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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