Simplex Distribution Family Function
The two parameters of the univariate standard simplex distribution are estimated by full maximum likelihood estimation.
simplex(lmu = "logitlink", lsigma = "loglink", imu = NULL, isigma = NULL,
imethod = 1, ishrinkage = 0.95, zero = "sigma")lmu, lsigma |
Link function for |
imu, isigma |
Optional initial values for |
imethod, ishrinkage, zero |
See |
The probability density function can be written
f(y; mu, sigma) = [2* pi * sigma^2 * (y*(1-y))^3]^(-0.5) * exp[-0.5 * (y-mu)^2 / (sigma^2 * y * (1-y) * mu^2 * (1-mu)^2)]
for 0 < y < 1,
0 < mu < 1,
and sigma > 0.
The mean of Y is mu (called mu, and
returned as the fitted values).
The second parameter, sigma, of this standard simplex
distribution is known as the dispersion parameter.
The unit variance function is
V(mu) = mu^3 (1-mu)^3.
Fisher scoring is applied to both parameters.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
This distribution is potentially useful for dispersion modelling.
Numerical problems may occur when mu is very close to 0 or 1.
T. W. Yee
Jorgensen, B. (1997). The Theory of Dispersion Models. London: Chapman & Hall
Song, P. X.-K. (2007). Correlated Data Analysis: Modeling, Analytics, and Applications. Springer.
sdata <- data.frame(x2 = runif(nn <- 1000))
sdata <- transform(sdata, eta1 = 1 + 2 * x2,
eta2 = 1 - 2 * x2)
sdata <- transform(sdata, y = rsimplex(nn, mu = logitlink(eta1, inverse = TRUE),
dispersion = exp(eta2)))
(fit <- vglm(y ~ x2, simplex(zero = NULL), data = sdata, trace = TRUE))
coef(fit, matrix = TRUE)
summary(fit)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.