distribution of the mean induced by a Dirichlet distribution

Suppose I have a Dirichlet distribution, D, defined by parameters a1,
a2, ..., ak, which describe the Bayesian probability that p1, p2, ...,
pk are the parameters of some multinomial distribution, M.

The categories of the multinomial distribution represent monetary
values. For example, p3 represents the probability of $3. For this
reason, it makes sense to talk about the expected value of the
multinomial distribution, in the following sense:

E[M] = sum(1*p1 + 2*p2 + ... k*pk)

I would like to compute the distribution of E[M] from the Dirichlet
distribution. Is there an analytical solution to this problem?

Any help would be greatly appreciated,
Daniel Stutzbach, Ph.D.

.

Relevant Pages

  • Re: distribution of the mean induced by a Dirichlet distribution
    ... pk are the parameters of some multinomial distribution, ... Is there an analytical solution to this problem? ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.math)
  • Re: distribution of the mean induced by a Dirichlet distribution
    ... On Sep 21, 1:20 am, Daniel Stutzbach ... The categories of the multinomial distribution represent monetary ... I would like to compute the distribution of Efrom the Dirichlet ... I don't think there is an analytical solution, ...
    (sci.stat.math)