Inverse Gaussian Distribution Family Function
Estimates the two parameters of the inverse Gaussian distribution by maximum likelihood estimation.
inv.gaussianff(lmu = "loglink", llambda = "loglink",
imethod = 1, ilambda = NULL,
parallel = FALSE, ishrinkage = 0.99, zero = NULL)lmu, llambda |
Parameter link functions for the mu and
lambda parameters.
See |
ilambda, parallel |
See |
imethod, ishrinkage, zero |
See |
The standard (“canonical”) form of the inverse Gaussian distribution has a density that can be written as
f(y;mu,lambda) = sqrt(lambda/(2*pi*y^3)) * exp(-lambda*(y-mu)^2/(2*y*mu^2))
where y>0, mu>0, and lambda>0. The mean of Y is mu and its variance is mu^3/lambda. By default, eta1=log(mu) and eta2=log(lambda). The mean is returned as the fitted values. This VGAM family function can handle multiple responses (inputted as a matrix).
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm
and vgam.
The inverse Gaussian distribution can be fitted (to a certain extent) using the usual GLM framework involving a scale parameter. This family function is different from that approach in that it estimates both parameters by full maximum likelihood estimation.
T. W. Yee
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
The R package SuppDists has several functions for evaluating the density, distribution function, quantile function and generating random numbers from the inverse Gaussian distribution.
idata <- data.frame(x2 = runif(nn <- 1000))
idata <- transform(idata, mymu = exp(2 + 1 * x2),
Lambda = exp(2 + 1 * x2))
idata <- transform(idata, y = rinv.gaussian(nn, mu = mymu, lambda = Lambda))
fit1 <- vglm(y ~ x2, inv.gaussianff, data = idata, trace = TRUE)
rrig <- rrvglm(y ~ x2, inv.gaussianff, data = idata, trace = TRUE)
coef(fit1, matrix = TRUE)
coef(rrig, matrix = TRUE)
Coef(rrig)
summary(fit1)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.