VGAM (version 0.9-0)

gamma1: 1-parameter Gamma Distribution

Description

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

Usage

gamma1(link = "loge", zero = NULL)

Arguments

link

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

zero

Details at CommonVGAMffArguments.

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 $$f(y)=\exp (-y)\times y^{shape-1}/\mathrm{\Gamma }(shape)$$ 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, lindley.

Examples

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