## maximum of a Dirichlet vector

An intriguing question on Stack Exchange this weekend, about the distribution of max{p¹,p²,…}the maximum component of a Dirichlet vector Dir(a¹,a²,…) with arbitrary hyper-parameters. Writing the density of this random variable is feasible, using its connection with a Gamma vector, but I could not find a closed-form expression. If there is such an expression, it may follow from the many properties of the Dirichlet distribution and I’d be interested in learning about it. (Very nice stamp, by the way! I wonder if the original formula was made with LaTeX…)

### 4 Responses to “maximum of a Dirichlet vector”

1. What if we assume a flat Dirichlet? a_1 = a_2 = … = 1

• Sure, for such a special case, there is a resolution.

2. Georges Henry Says:

Sans espoir. Meme pour une Dirichlet d’ordre 2 tu demandes le calcul explicite de

$\int_c^{1/c}\dfrac{t^{a_1-1}}{(1+t)^{a_1+a_2}}dt$

pas faisable en general.

• Merci de cette prompte réponse!

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