Density function and random generation for Dirichlet distribution with
parameter vector alpha.
Usage
rdirichlet(n, alpha)
ddirichlet(x, alpha, log = FALSE, tol = 1e-10)
Arguments
n
number of random variables to be generated.
alpha
vector of Dirichlet hyper parameter.
x
vector (or matrix) of points in sample space.
log
logical; if TRUE, natural logarithm of density is returned.
tol
tolerance of vectors not summing to 1 and negative values.
Value
rdirichlet returns a matrix, each row of which is an independent draw
from a Dirichlet distribution with parameter vector alpha.
ddirichlet returns a vector, each entry being the density of the
corresponding row of x. If x is a vector, then the output
will have length 1.
Details
If x is a matrix, each row is taken to be a different point whose
density is to be evaluated. If the number of columns in (or length of, in the
case of a vector) x is one less than the length of alpha, the
remaining column (or entry) is assumed to make the vector sum to 1.
The k-dimensional Dirichlet distribution has density
$$\frac{\Gamma\left(\sum_i \alpha_i\right)}{\prod_i \Gamma(\alpha_i)} \prod_{i=1}^k x_i^{\alpha_i-1}$$
assuming that \(x_i > 0\) and \(\sum_i x_i = 1\), and zero otherwise.
If the sum of row entries in x differs from 1 by more than tol,
or any entry takes a value less than -tol, the density is assumed to be
zero.
# NOT RUN {x = rdirichlet(10, c(1,2,3))
x
# Find densities at random points.ddirichlet(x, c(1,2,3))
# Last column to be inferred.ddirichlet(x[,c(1,2)], c(1,2,3))
# }