Density and and random generation for the Dirichlet distribution.
Usage
ddirichlet(x, alpha, log = FALSE)
rdirichlet(n, alpha)
Arguments
- x
vector or matrix of quantiles. If x is a vector, it needs to sum to one.
If x is a matrix, each row should sum to one.
- alpha
vector or matrix of positive shape parameters
- log
logical; if TRUE, densities \(p\) are returned as \(\log(p)\).
- n
number of random values to return.
Value
ddirichlet gives the density, rdirichlet generates random deviates.
Details
This implementation of ddirichlet allows for automatic differentiation with RTMB.
$$f(\mathbf{x};\,\boldsymbol{\alpha}) = \frac{\Gamma\!\left(\sum_i \alpha_i\right)}{\prod_i \Gamma(\alpha_i)} \prod_i x_i^{\alpha_i - 1},$$
where \(\mathbf{x}\) lies on the unit simplex and \(\alpha_i > 0\).
Examples
# single alpha
alpha <- c(1,2,3)
x <- rdirichlet(1, alpha)
d <- ddirichlet(x, alpha)
# vectorised over alpha
alpha <- rbind(alpha, 2*alpha)
x <- rdirichlet(2, alpha)