Generate Random Observations from the Simplex Distribution

Generates independent observations from a simplex distribution \(S^{-1}(\mu, \sigma^2)\) using the representation via inverse-Gaussian and chi-squared random variables (Michael, Schucany & Haas, 1976).

Usage

rsimplex(n, mu, sigma2)

Arguments

n

Integer; number of observations.

mu

Numeric scalar or vector of means in (0, 1).

sigma2

Numeric scalar or vector of dispersion parameters (> 0).

Value

Numeric vector of length n with values in (0, 1).

Details

Uses the reparametrisation \(\epsilon = \mu/(1-\mu)\) (odds) and \(\tau = \sigma^2 (1-\mu)^2\) to generate from an inverse-Gaussian mixture. Identical algorithm to the Ox reference implementation.

References

Barndorff-Nielsen O.E., Jorgensen B. (1991). Some parametric models on the simplex. Journal of Multivariate Analysis, 39(1), 106–116.

Michael J.R., Schucany W.R., Haas R.W. (1976). Generating random variates using transformations with multiple roots. The American Statistician, 30(2), 88–90.

Examples

set.seed(1)
y <- rsimplex(200, mu = 0.3, sigma2 = 2)
hist(y, breaks = 20, main = "Simplex(0.3, 2)")