VGAM (version 1.1-12)

Simplex : Simplex Distribution

Description

Density function, and random generation for the simplex distribution.

Usage

dsimplex(x, mu = 0.5, dispersion = 1, log = FALSE)
rsimplex(n, mu = 0.5, dispersion = 1)

Value

dsimplex(x) gives the density function,

rsimplex(n) gives \(n\) random variates.

Arguments

x

Vector of quantiles. The support of the distribution is the interval \((0,1)\).

mu, dispersion

Mean and dispersion parameters. The former lies in the interval \((0,1)\) and the latter is positive.

n, log

Same usage as runif.

Author

T. W. Yee

Details

The VGAM family function simplex fits this model; see that online help for more information. For rsimplex() the rejection method is used; it may be very slow if the density is highly peaked, and will fail if the density asymptotes at the boundary.

See Also

simplex.

Examples

sigma <- c(4, 2, 1)  # Dispersion parameter
mymu  <- c(0.1, 0.5, 0.7); xxx <- seq(0, 1, len = 501)
if (FALSE)  par(mfrow = c(3, 3))  # Figure 2.1 of Song (2007)
for (iii in 1:3)
  for (jjj in 1:3) {
    plot(xxx, dsimplex(xxx, mymu[jjj], sigma[iii]),
         type = "l", col = "blue", xlab = "", ylab = "", main =
         paste("mu = ", mymu[jjj], ", sigma = ", sigma[iii], sep = "")) }