VGAM (version 1.1-14)

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.

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, gammaff.mm.

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)