Wald Distribution Family Function
Estimates the parameter of the standard Wald distribution by maximum likelihood estimation.
waldff(llambda = "loglink", ilambda = NULL)
llambda,ilambda |
See |
The standard Wald distribution is a special case of the inverse Gaussian distribution with mu=1. It has a density that can be written as
f(y;mu,lambda) = sqrt(lambda/(2*pi*y^3)) * exp(-lambda*(y-1)^2/(2*y))
where y>0 and lambda>0. The mean of Y is 1 (returned as the fitted values) and its variance is 1/lambda. By default, eta=log(lambda).
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
The VGAM family function inv.gaussianff
estimates the location parameter mu too.
T. W. Yee
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.
wdata <- data.frame(y = rinv.gaussian(n = 1000, mu = 1, lambda = exp(1))) wfit <- vglm(y ~ 1, waldff(ilambda = 0.2), data = wdata, trace = TRUE) coef(wfit, matrix = TRUE) Coef(wfit) summary(wfit)
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