Re: distribution of the mean induced by a Dirichlet distribution

On Sep 21, 1:20 am, Daniel Stutzbach <daniel.stutzb...@xxxxxxxxx>
wrote:
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.

I don't think there is an analytical solution, but Monte Carlo will
help
you for a particular application. Just simulation from the Dirichlet
Distribution, and calculate the average of the sample weighted sums.


.

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