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power of logistic distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126913] power of logistic distribution
  • From: paul <paulvonhippel at yahoo.com>
  • Date: Sun, 17 Jun 2012 03:58:21 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I would like an expression for the mean of a variable that is some integer power of a logistic variable. I have tried the following approach, which did not work. Many thanks for any suggestions.

Here is what I've done so far. If I specify the power (e.g., power=2), Mathematica returns an answer rather quickly -- e.g., 

In[66]:= Mean[TransformedDistribution[Z^2, 
   Z \[Distributed] LogisticDistribution[\[Mu], \[Sigma]]]]
Out[66]= 1/3 (3 \[Mu]^2 + \[Pi]^2 \[Sigma]^2)

I get quick results if the power is 2, 3, 4, ..., 100. So it seems to me there must be some general solution for integer powers. But when I ask for that general solution, Mathematica simply echoes the input:

In[64]:= Assuming[p \[Element] Integers, 
  Mean[TransformedDistribution[Z^p, 
    Z \[Distributed] LogisticDistribution[\[Mu], \[Sigma]]]]]
Out[64]= Mean[
 TransformedDistribution[\[FormalX]^
  p, \[FormalX] \[Distributed] LogisticDistribution[\[Mu], \[Sigma]]]]

Why isn't it giving me something more digested?



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