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

David Winsemius dwinsemius at comcast.net
Tue May 9 22:17:31 CEST 2017

```> 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>______________________________________________
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