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
range of draws runs its own generator, seeded from R's stream, so that
set.seed() governs the result; the seeding does depend on how the work
is split, so reproducing a value also requires the same
RcppParallel::setThreadOptions().
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