In probability and statistics, the **Dirichlet distribution** (after Johann Peter Gustav Lejeune Dirichlet), often denoted, is a family of continuous multivariate probability distributions parametrized by a vector of positive reals. It is the multivariate generalization of the beta distribution. Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. That is, its probability density function returns the belief that the probabilities of *K* rival events are given that each event has been observed times.

The infinite-dimensional generalization of the Dirichlet distribution is the *Dirichlet process*.

Read more about Dirichlet Distribution: Probability Density Function, Related Distributions, Applications

### Other articles related to "distribution, dirichlet distribution, dirichlet distributions, distributions, dirichlet":

... themselves can either be discrete (typically generated from a categorical

**distribution**) or continuous (typically from a Gaussian

**distribution**) ... and observed variables follow a Gaussian

**distribution**... Hidden Markov models are generative models, in which the joint

**distribution**of observations and hidden states, or equivalently both the prior ...

**Dirichlet Distribution**- Intuitive Interpretations of The Parameters - Pólya's Urn

... To see that this limiting vector has the above

**Dirichlet distribution**, check that all mixed moments agree ... also help explain how small α values yield

**Dirichlet distributions**with most of the probability mass concentrated around a single point on the simplex ...

... The rule of succession comes from setting a binomial likelihood, and a uniform prior

**distribution**... forward generalisation is just the multivariate extensions of these two

**distributions**1)Setting a uniform prior over the initial m categories, and 2) using the ... It can be shown that the uniform

**distribution**is a special case of the

**Dirichlet distribution**with all of its parameters equal to 1 (just as the uniform is Beta(1,1) in the ...

**Dirichlet Distribution**

... In statistics, the generalized

**Dirichlet distribution**(GD) is a generalization of the

**Dirichlet distribution**with a more general covariance structure and almost twice the number of parameters ... Random variables with a GD

**distribution**are neutral ... This reduces to the standard

**Dirichlet distribution**if for ( is arbitrary) ...

... See also

**Dirichlet**-multinomial

**distribution**Learning the various

**distributions**(the set of topics, their associated word probabilities, the topic of each word, and the particular topic mixture ... used a variational Bayes approximation of the posterior

**distribution**alternative inference techniques use Gibbs sampling and expectation propagation ... the probabilities in the above equation by the true

**distribution**expression to write out the explicit equation Let be the number of word tokens in the document with the same ...

### Famous quotes containing the word distribution:

“In this *distribution* of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”

—Ralph Waldo Emerson (1803–1882)