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 |
Link function applied to the (positive) shape parameter.
See |
zero, parallel |
Details at |
type.fitted, percentiles |
See |
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 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.
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.
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) Coef(fit) summary(fit)
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