Simulates from a Dirichlet distribution with concentration parameter vector \(\alpha\) = (\(\alpha_1\), ..., \(\alpha_K\)).
rDir(n = 1, alpha = c(1, 1))A numeric scalar. The size of sample required.
A numeric vector. Dirichlet concentration parameter.
An n by length(alpha) numeric matrix.
The simulation is based on the property that if \(Y_1, \ldots, Y_K\) are independent, \(Y_i\) has a gamma(\(\alpha_i\), 1) distribution and \(S = Y_1 + \cdots + Y_k\) then \((Y_1, \ldots, Y_K) / S\) has a Dirichlet(\(\alpha_1\), ..., \(\alpha_K\)) distribution.
See https://en.wikipedia.org/wiki/Dirichlet_distribution#Gamma_distribution
Kotz, S., Balakrishnan, N. and Johnson, N. L. (2000) Continuous Multivariate Distributions, vol. 1, Models and Applications, 2nd edn, ch. 49. New York: Wiley. doi:10.1002/0471722065
rprior_prob for prior simulation of
GEV parameters - prior on probability scale.
rDir(n = 10, alpha = 1:4)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.115370906 0.01462583 0.23753035 0.6324729
#> [2,] 0.049415940 0.49527651 0.09582583 0.3594817
#> [3,] 0.028259268 0.11340945 0.24134632 0.6169850
#> [4,] 0.123849100 0.23267500 0.32954730 0.3139286
#> [5,] 0.063862382 0.12346098 0.17856201 0.6341146
#> [6,] 0.079358460 0.14770560 0.25000066 0.5229353
#> [7,] 0.001612992 0.24626422 0.07988016 0.6722426
#> [8,] 0.080030390 0.02010660 0.45993851 0.4399245
#> [9,] 0.023265218 0.29859926 0.42866548 0.2494700
#> [10,] 0.037039164 0.02016963 0.23130954 0.7114817