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

Czarek Kowalski czarek230800 at gmail.com
Tue May 9 23:05:09 CEST 2017

```I have already posted that in attachement - pdf file. I am posting
plain text here:

> library(tmvtnorm)

> meann = c(55, 40, 50, 35, 45, 30)

> covv = matrix(c(  1, 1, 0, 2, -1, -1,

+                   1, 16, -6, -6, -2, 12,

+                   0, -6, 4, 2, -2, -5,

+                   2, -6, 2, 25, 0, -17,

+                  -1, -2, -2, 0, 9, -5,

+                  -1, 12, -5, -17, -5, 36), 6, 6)

> df = 4

> lower = c(20, 20, 20, 20, 20, 20)

> upper = c(60, 60, 60, 60, 60, 60)

> X1 <- rtmvt(n=100000, meann, covv, df, lower, upper)

> sum(X1[,1]) / 100000

[1] 54.98258

> sum(X1[,2]) / 100000

[1] 40.36153

> sum(X1[,3]) / 100000

[1] 49.83571

> sum(X1[,4]) / 100000

[1] 34.69571      # "4th element of mean vector"

> sum(X1[,5]) / 100000

[1] 44.81081

> sum(X1[,6]) / 100000

[1] 31.10834

And corresponding results received using equation (3) from pdf file:
[54.97,
40,
49.95,
35.31, #  "4th element of mean vector"
44.94,
31.32]

On 9 May 2017 at 22:17, David Winsemius <dwinsemius at comcast.net> wrote:
>
>> On May 9, 2017, at 1:11 PM, Czarek Kowalski <czarek230800 at gmail.com> wrote:
>>
>> Of course I have expected the difference between theory and a sample
>> of realizations of RV's and result mean should still be a random
>> variable. But, for example for 4th element of mean vector: 35.31 -
>> 34.69571 = 0.61429. It is quite big difference, nieprawdaż? I have
>> expected that the difference would be smaller because of law of large
>> numbers (for 10mln samples the difference is quite similar).
>
> I for one have no idea what is meant by a "4th element of mean vector". So I have now idea what to consider "big". I have found that my intuitions about multivariate distributions, especially those where the covariate structure is as complex as you have assumed, are often far from simulated results.
>
> I suggest you post some code and results.
>
> --
> David.
>
>
>>
>> On 9 May 2017 at 21:40, David Winsemius <dwinsemius at comcast.net> wrote:
>>>
>>>> On May 9, 2017, at 10:09 AM, 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?
>>>
>>> I guess the question is why you would NOT expect a difference between theory and a sample of realizations of RV's? The result mean should still be a random variable, night wahr?
>>>
>>>
>>>> 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.
>>>
>>> David Winsemius
>>> Alameda, CA, USA
>>>
>
> David Winsemius
> Alameda, CA, USA
>

```