Dirichlet Density Function

A Dirichlet Density Function is a Continuous Multivariate Probability Density Function parametrized by the Vector (α) of Positive Real Numbers.

• AKA: Dirichlet Density, Dirichlet Probability Density Function.
• Context:
  • It is a multivariate generalization of the Beta Density Function.
  • It is named after Johann Peter Gustav Lejeune Dirichlet.
• See: Dirichlet Distribution Function, Dirichlet Process.

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References

2009

• http://en.wikipedia.org/wiki/Dirichlet_distribution
  • In probability and statistics, the Dirichlet distribution (after Johann Peter Gustav Lejeune Dirichlet), often denoted Dir(α), is a family of continuous multivariate probability distributions parametrized by the vector α of positive reals. It is the multivariate generalization of the beta distribution, and conjugate prior of the categorical distribution and multinomial distribution in Bayesian statistics. That is, its probability density function returns the belief that the probabilities of [math]\displaystyle{ K }[/math] rival events are [math]\displaystyle{ x_i }[/math] given that each event has been observed [math]\displaystyle{ \alpha_i-1 }[/math] times.

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