VGAM (version 0.9-1)

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)

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.

Value

• dsimplex(x) gives the density function, rsimplex(n) gives $n$ random variates.

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)
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 = "")) }