VGAM (version 0.8-4.1)

gamma1: 1-parameter Gamma Distribution

Description

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

Usage

gamma1(link = "loge", earg=list())

Arguments

link

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

earg

List. Extra argument for the link. See earg in Links for general information.

Value

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

Details

The density function is given by $$f(y) = \exp(-y) \times y^{shape-1} / \Gamma(shape)$$ 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 $\sigma^2 = shape$.

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, lgammaff.

Examples

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