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?

**Follow-Ups**:**Re: power of logistic distribution***From:*Bob Hanlon <hanlonr357@gmail.com>