In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted ⁡ (), is a family of continuous multivariate probability distributions parameterized by a vector of positive reals.

2024年12月19日 · The Dirichlet distribution Dir(α) is a family of continuous multivariate probability distributions, parameterized by a vector α of positive reals. Here’s an introduction to the Dirichlet distribution and how to use it in statistical analysis.

A Dirichlet distribution (pronounced Deer-eesh-lay) is a way to model random probability mass functions (PMFs) for finite sets. The distribution creates n positive numbers (a set of random vectors X 1 …X n ) that add up to 1; Therefore, it is closely related to the multinomial distribution , which also requires n numbers that sum to 1.

The Dirichlet distribution explained, with detailed derivations of the mean vector and the covariance matrix, and proofs of other important results.

Dirichlet process is a model for a stream of symbols that 1) satisfies the exchangeability rule and that 2) allows the vocabulary of symbols to grow without limit.

First, we note an important relation between the Dirichlet distribution and the Gamma distribution, which is used to generate random vectors which are Dirichlet distributed. If, for i ∈ {1,2,··· ,K},

This tutorial covers the Dirichlet distribution, Dirichlet process, P olya urn (and the associated Chinese restaurant process), hierarchical Dirichlet Process, and the Indian bu et process. Apart from basic properties, we describe and contrast three methods of generating samples: stick-breaking, the P olya urn, and drawing gamma random variables.

2023年4月8日 · The Dirichlet distribution plays an important role in the theory of order statistics. For instance, if $ X _ {1}, \ldots, X _ {n} $ are independent random variables that are uniformly distributed over the interval $ [ 0, 1] $ and $ X ^ {( 1)} \leq \dots \leq X ^ {( n)} $ are the corresponding order statistics (cf. Order statistic ), the joint ...

2024年12月23日 · The Dirichlet distribution is a generalization of the Beta distribution. It is a probability distribution describing probabilities of outcomes. Instead of describing probability of one of two outcomes of a Bernoulli trial, like the Beta distribution does, it …

2023年8月1日 · The Dirichlet distribution is a generalization of the beta distribution. In Bayesian statistics, it is commonly used as the conjugate prior to the multinomial distribution, hence it can be used to model the uncertainty of a random vector of probabilities.