Related Distributions
If, for
then
and
Although the Xis are not independent from one another, they can be seen to be generated from a set of independent gamma random variables (see for proof). Unfortunately, since the sum is lost in forming X, it is not possible to recover the original gamma random variables from these values alone. Nevertheless, because independent random variables are simpler to work with, this reparametrization can still be useful for proofs about properties of the Dirichlet distribution.
Read more about this topic: Dirichlet Distribution
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