gamma1 {VGAM}R Documentation

1-parameter Gamma Distribution

Description

Estimates the 1-parameter gamma distribution by maximum likelihood estimation.

Usage

gamma1(link = "loge")

Arguments

link Link function applied to the (positive) shape parameter. See Links for more choices.

Details

The density function is given by

f(y) = exp(-y) y^(shape-1) / gamma(shape)

for shape > 0 and y > 0. Here, gamma(shape) is the gamma function, as in gamma. The mean of Y (returned as the fitted values) is mu=shape, and the variance is sigma^2 = shape.

Value

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

Note

This VGAM family function can handle a multivariate (matrix) response.

The parameter shape matches with shape in rgamma. The argument rate in rgamma is assumed 1 for this family function.

If rate is unknown use the family function gamma2.ab to estimate it too.

Author(s)

T. W. Yee

References

Most standard texts on statistical distributions describe the 1-parameter gamma distribution, e.g.,

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

See Also

gamma2.ab for the 2-parameter gamma distribution.

Examples

y = rgamma(n=100, shape= exp(3))
fit = vglm(y ~ 1, gamma1, trace=TRUE, crit="c")
coef(fit, matrix=TRUE)
Coef(fit)
summary(fit)

[Package VGAM version 0.7-1 Index]