VGAM (version 1.1-8)

gamma1: 1-parameter Gamma Regression Family Function

Description

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

Usage

gamma1(link = "loglink", zero = NULL, parallel = FALSE,
       type.fitted = c("mean", "percentiles", "Qlink"),
       percentiles = 50)

Value

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

and vgam.

Arguments

link

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

zero, parallel

Details at CommonVGAMffArguments.

type.fitted, percentiles

See CommonVGAMffArguments for information. Using "Qlink" is for quantile-links in VGAMextra.

Author

T. W. Yee

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 default 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.,

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

See Also

gammaR for the 2-parameter gamma distribution, lgamma1, lindley, simulate.vlm.

Examples

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