Density, random generation, and basic utilities for the Dirichlet distribution.
Usage
ddirichlet(x, concentration, log = FALSE)
pdirichlet(q, concentration, R = 100000)
rdirichlet(n, concentration)
qdirichlet(p, concentration, ...)Arguments
- x
numeric vector or matrix (rows sum to 1).
- concentration
numeric vector of concentration parameters (> 0).
- log
logical; return log-density if TRUE.
- q
numeric vector of quantiles.
- R
number of Monte Carlo simulations used to approximate the CDF. Must be at most
.Machine$integer.max.- n
number of samples.
- p
numeric vector of probabilities; accepted by
qdirichlet()only to give a meaningful error, see below.- ...
further arguments, accepted by
qdirichlet()and ignored.
Value
ddirichlet() gives a numeric vector of densities (one per
row of x), pdirichlet() gives an approximate probability,
and rdirichlet() generates a matrix with n rows of random
deviates. qdirichlet() only signals an error, as no unique
multivariate quantile function exists; it takes the same arguments as
the others so that the message is reached rather than an argument
mismatch.
Details
The Dirichlet distribution is a multivariate generalization of the Beta distribution defined on the simplex: $$\sum_{i=1}^k x_i = 1, \quad x_i \ge 0$$
Random number generation
pdirichlet() evaluates the CDF by simulation and is parallelised. Each
fixed block of draws runs its own generator, seeded from R's stream, so
that set.seed() alone reproduces the result, independently of the
number of threads.
Examples
ddirichlet(c(0.2, 0.3, 0.5), c(1,1,1))
#> [1] 2
pdirichlet(c(0.2, 0.3, 0.5), c(1,1,1))
#> [1] 0
rdirichlet(5, c(1,1,1))
#> [,1] [,2] [,3]
#> [1,] 0.007664882 0.45423051 0.53810461
#> [2,] 0.406895342 0.57088656 0.02221810
#> [3,] 0.335196674 0.62893638 0.03586694
#> [4,] 0.417697775 0.08456334 0.49773888
#> [5,] 0.005668935 0.88696625 0.10736481