The Dirichlet distribution on the simplex.
dDirichlet(x, alpha, log=FALSE, measure="Lebesgue")
rDirichlet.acomp(n, alpha)
rDirichlet.rcomp(n, alpha)For rDirichlet.* a generated random dataset of class "acomp" or "rcomp",
drawn from a Dirichlet distribution with the given parameter
alpha. The names of alpha are used to name the parts.
For dDirichlet, the (conventional) Dirichlet density
number of datasets to be simulated
parameters of the Dirichlet distribution
a data set (acomp, rcomp, data.frame, matrix; even one-row) of point(s) on the simplex
a boolean, controlling if the density or the log-density is returned
one of: "Lebesgue" or "Aitchison" (partial match applies), or else a function returning the reference LOG-density (see details below)
K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado
The Dirichlet distribution is the result of closing a vector of equally-scaled Gamma-distributed variables. It the conjugate prior distribution for a vector of probabilities of a multinomial distribution. Thus, it generalizes the beta distribution for more than two parts.
For the density, the implementation allows to obtain the conventional density
(with respect to the Lebesgue measure, default behaviour or giving
measure="Lebuesgue"), the compositional density (with respect to the
Aitchison measure, giving measure="Aitchison"), or else w.r.to any other
reference density (giving at measure a function returning the log-density
of the reference measure for any point of the simplex)
Aitchison, J. (1986) The Statistical Analysis of Compositional
Data Monographs on Statistics and Applied Probability. Chapman &
Hall Ltd., London (UK). 416p.
Mateu-Figueras, G.; Pawlowsky-Glahn, V. (2005). The Dirichlet distribution
with respect to the Aitchison measure on the simplex, a first approach.
In: Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.)
Proceedings of the 2nd International Workshop on Compositional Data Analysis,
Universitat de Girona, ISBN 84-8458-222-1, http://ima.udg.es/Activitats/CoDaWork05/
rnorm.acomp
tmp <- rDirichlet.acomp(10,alpha=c(A=2,B=0.2,C=0.2))
plot(tmp)
dDirichlet(tmp, alpha=c(A=2,B=0.2,C=0.2))
dDirichlet(tmp[1,]*0, alpha=c(A=2,B=0.2,C=0.2))
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