1-parameter Gamma Distribution

Description

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

Usage

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

Arguments

Details

The density function is given by

f(y) = exp(-y) 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.

Value

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

Note

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.

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

Author(s)

T. W. Yee

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)

Results