truncated distributions

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truncated distributions

statfan
I am sampling from the truncated multivariate student t distribution "rtmvt" in the package {tmvtnorm}. My question is about the mean vector.  Is it possible to define a mean vector outside of the truncated region? Thank you in advance for any help.
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Re: truncated distributions

David Winsemius

On Apr 2, 2011, at 11:06 AM, statfan wrote:

> I am sampling from the truncated multivariate student t distribution  
> "rtmvt"
> in the package {tmvtnorm}. My question is about the mean vector.  Is  
> it
> possible to define a mean vector outside of the truncated region?  
> Thank you
> in advance for any help.

In what sense are you interpreting the word "mean"? The "mean" in the  
specification of a truncated distribution is probably not going to be  
the expected value of a random variable from such a distribution, but  
rather refers to the parent distribution's mean.

 > print(x=rtmvnorm(10, mean=0, sigma=1, lower=0.5, upper=1), digits=3)
        [,1]
  [1,] 0.984
  [2,] 0.528
  [3,] 0.529
  [4,] 0.550
  [5,] 0.832
  [6,] 0.788
  [7,] 0.775
  [8,] 0.631
  [9,] 0.832
[10,] 0.558
--

David Winsemius, MD
West Hartford, CT

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Re: truncated distributions

statfan
The definition of the "mean vector" is essentially what my question boils down to.  In the functions details, the author states

"We sample x ~ T(mean, Sigma, df) subject to the rectangular truncation lower <= x <= upper. Currently, two random number generation methods are implemented: rejection sampling and the Gibbs Sampler."

So if the mean vector in the "rtmvt" function is the mean of the parent distribution's mean (as I hope it is), then it would be acceptable to define a mean vector outside of the truncated range.  Clarification of this point would be greatly appreciated.  
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Re: truncated distributions

David Winsemius

On Apr 2, 2011, at 1:15 PM, statfan wrote:

> The definition of the "mean vector" is essentially what my question  
> boils
> down to.  In the functions details, the author states
>
> "We sample x ~ T(mean, Sigma, df) subject to the rectangular  
> truncation
> lower <= x <= upper. Currently, two random number generation methods  
> are
> implemented: rejection sampling and the Gibbs Sampler."
>
> So if the mean vector in the "rtmvt" function is the mean of the  
> parent
> distribution's mean (as I hope it is),

Given the results of what I posted earlier ... how could it be  
otherwise?

> then it would be acceptable to define
> a mean vector outside of the truncated range.  Clarification of this  
> point
> would be greatly appreciated.
>
> --
> View this message in context: http://r.789695.n4.nabble.com/truncated-distributions-tp3422245p3422434.html
> Sent from the R help mailing list archive at Nabble.com.


--
David Winsemius, MD
West Hartford, CT

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.