The Dirichlet Distribution
Density and random generation for the Dirichlet distribution.
ddirichlet(probabilities, nu, logscale = FALSE) rdirichlet(n, nu)
probabilities |
A vector representing a discrete probability distribution, or a matrix where each row is a discrete probability distribution. Zero probabilities are not allowed. |
nu |
The parameters of the Dirichlet distribution. This can be a
vector of positive numbers, interpretable as prior counts, of length
matching the dimension of probabilities. If |
logscale |
Logical. If TRUE then return the density on the log scale. Otherwise return the density on the raw scale. |
n |
The number of desired draws. |
The Dirichlet distribution is a generalization of the beta distribution. Whereas beta distribution is a model for probabilities, the Dirichlet distribution is a model for discrete distributions with several possible outcome values.
Let pi denote a discrete probability distribution (a vector of positive numbers summing to 1), and let nu be a vector of positive numbers (the parameters of the Dirichlet distribution), which can be thought of as prior counts. Then the density of the Dirichlet distribution can be written
(gamma(sum(nu)) / prod(gamma(nu))) prod(pi^(nu - 1)).
ddirichlet returns a vector of density values, with one
entry per row in probabilities. rdirichlet returns a
matrix (if n > 1) or a vector (if n==1) containing the
draws from the Dirichlet distribution with the specified parameters.
Steven L. Scott steve.the.bayesian@gmail.com
Gelman, Carlin, Stern, Rubin (2003), "Bayesian Data Analysis", Chapman and Hall.
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