waldff: Wald Distribution Family Function

In VGAM: Vector Generalized Linear and Additive Models

Wald Distribution Family Function

Description

Estimates the parameter of the standard Wald distribution by maximum likelihood estimation.

Usage

waldff(llambda = "loglink", ilambda = NULL)

Arguments

llambda, ilambda

See CommonVGAMffArguments for information.

Details

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;\lambda) = \sqrt{\lambda/(2\pi y^3)} \; \exp\left(-\lambda (y-1)^2/(2 y)\right)

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).

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Note

The VGAM family function inv.gaussianff estimates the location parameter \mu too.

Author(s)

T. W. Yee

References

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.

See Also

inv.gaussianff, rinv.gaussian.

Examples

wdata <- data.frame(y = rinv.gaussian(1000, mu =  1, exp(1)))
wfit <- vglm(y ~ 1, waldff(ilambda = 0.2), wdata, trace = TRUE)
coef(wfit, matrix = TRUE)
Coef(wfit)
summary(wfit)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.