# Sum of Dirichlet distributions

by Rubertos   Last Updated October 10, 2019 03:20 AM - source

Let $$\alpha\in (0,\infty)^n$$ and $$\{e_1,...,e_n\}$$ be the standard ordered basis for $$\mathbb{R}^n$$, and define $$\alpha_0:=\sum_{i=1}^n \alpha_i$$.

Let $$Dir(\alpha+e_k)$$ be Dirichlet distributions and $$\mu_k$$ be its distribution measures.

Then, how do I show that $$\sum_{i=1}^n \frac{\alpha_i}{\alpha_0} \mu_k$$ is the distribution measure of $$Dir(\alpha)$$?