dirichlet: Dirichlet distribution and generalizations

Description

The Dirichlet distribution in likelihood (for p) form, including the generalized Dirichlet distribution due to Connor and Mosimann

Usage

dirichlet(powers, alpha)
GD(alpha, beta, beta0=0)
GD_wong(alpha, beta)
rdirichlet(n,H)
is.dirichlet(H)
rp_unif(n,H)

Arguments

powers

In function dirichlet() a (named) vector of powers

alpha,beta

A vector of parameters for the Dirichlet or generalized Dirichlet distribution

beta0

In function GD(), an arbitrary parameter

Object of class hyper2

Number of observations

Details

These functions are really convenience functions.

Function rdirichlet() returns random samples drawn from a Dirichlet distribution. If second argument H is a hyper2 object, it is tested [with is.dirichlet()] for being a Dirichlet distribution. If so, samples from it are returned. If not, (e.g. icons), an error is given. If H is not a hyper2 object, it is interpreted as a vector of parameters \(\alpha\) [not a vector of powers].

Function rp_unif() returns uniformly distributed vectors, effectively using H*0; but note that this uses Dirichlet sampling which is much faster and better than the Metropolis-Hastings functionality documented at rp.Rd.

Functions GD() and GD_wong() return a likelihood function corresponding to the Generalized Dirichlet distribution as presented by Connor and Mosimann, and Wong, respectively. In GD_wong(), alpha and beta must be named vectors; the names of alpha give the names of \(x_1,\ldots,x_k\) and the last element of beta gives the name of \(x_{k+1}\).

References

R. J. Connor and J. E. Mosimann 1969. “Concepts of independence for proportions with a generalization of the Dirichlet distribution”. Journal of the American Statistical Association, 64:194--206
T.-T. Wong 1998. “Generalized Dirichlet distribution in Bayesian Analysis”. Applied Mathematics and Computation, 97:165--181

Examples

Run this code

# NOT RUN {
x1 <- dirichlet(c(a=1,b=2,c=3))
x2 <- dirichlet(c(c=3,d=4))

x1+x2

H <- dirichlet(c(a=1,b=2,c=3,d=4))
rdirichlet(10,H)
colMeans(rdirichlet(1e4,H))

# }