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truncated distributions

4 messages · David Winsemius, statfan

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

            

      
      
      
    

        
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

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      statfan
    

    

      
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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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      David Winsemius
    

    

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

        

            

      
      
      
    

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