gamma1: 1-parameter Gamma Regression Family Function

View source: R/family.univariate.R

gamma1R Documentation

1-parameter Gamma Regression Family Function


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


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



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.


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.


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


This VGAM family function can handle a multiple responses, which is inputted as a matrix.

The parameter shape matches with shape in rgamma. The argument rate in rgamma is assumed 1 for this family function, so that scale = 1 is used for calls to dgamma, qgamma, etc.

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


T. W. Yee


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,


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)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.