Distribution of Dirichlet <i>L</i>‐functions

Lecture 24 : Dirichlet distribution and Dirichlet Process

On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution an...

The Dirichlet-tree distribution

This note further explores the Dirichlet-tree distribution developed by Dennis (1991). An inclusion relationship is given for different tree structures and an independence relationship is given for probabilities in the tree. The posterior, evidence, and predictive density are derived for multinomial observations.

Hyperprior on symmetric Dirichlet distribution

In this article we introduce how to put vague hyperprior on Dirichlet distribution, and we update the parameter of it by adaptive rejection sampling (ARS). Finally we analyze this hyperprior in an over-fitted mixture model by some synthetic experiments.

Uniform Distribution of Zeros of Dirichlet Series

We consider a class of Dirichlet series which is more general than the Selberg class. Dirichlet series in this class, have meromorphic continuation to the whole plane and satisfy a certain functional equation. We prove, under the assumption of a certain hypothesis concerning the density of zeros on average, that the sequence formed by the imaginary parts of the zeros of a Dirichlet series in th...