VGAM (version 1.1-1)

gammaR: 2-parameter Gamma Distribution

Description

Estimates the 2-parameter gamma distribution by maximum likelihood estimation.

Usage

gammaR(lrate = "loglink", lshape = "loglink", irate = NULL,
       ishape = NULL, lss = TRUE, zero = "shape")

Arguments

lrate, lshape

Link functions applied to the (positive) rate and shape parameters. See Links for more choices.

irate, ishape

Optional initial values for rate and shape. A NULL means a value is computed internally. If a failure to converge occurs, try using these arguments.

zero, lss

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 $$f(y; rate, shape) = \exp(-rate \times y) \times y^{shape-1} \times rate^{shape} / \Gamma(shape)$$ for \(shape > 0\), \(rate > 0\) and \(y > 0\). Here, \(\Gamma(shape)\) is the gamma function, as in gamma. The mean of Y is \(\mu = shape/rate\) (returned as the fitted values) with variance \(\sigma^2 = \mu^2 /shape = shape/rate^2\). By default, the two linear/additive predictors are \(\eta_1 = \log(rate)\) and \(\eta_2 = \log(shape)\).

References

Most standard texts on statistical distributions describe the 2-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

gamma1 for the 1-parameter gamma distribution, gamma2 for another parameterization of the 2-parameter gamma distribution, bigamma.mckay for a bivariate gamma distribution, expexpff, simulate.vlm, rgamma, negloglink.

Examples

# NOT RUN {
# Essentially a 1-parameter gamma
gdata <- data.frame(y1 = rgamma(n <- 100, shape =  exp(1)))
fit1 <- vglm(y1 ~ 1, gamma1, data = gdata, trace = TRUE)
fit2 <- vglm(y1 ~ 1, gammaR, data = gdata, trace = TRUE, crit = "coef")
coef(fit2, matrix = TRUE)
Coef(fit2)

# Essentially a 2-parameter gamma
gdata <- data.frame(y2 = rgamma(n = 500, rate = exp(1), shape = exp(2)))
fit2 <- vglm(y2 ~ 1, gammaR, data = gdata, trace = TRUE, crit = "coef")
coef(fit2, matrix = TRUE)
Coef(fit2)
summary(fit2)
# }