gamma1 {VGAM} | R Documentation |
Estimates the 1-parameter gamma distribution by maximum likelihood estimation.
gamma1(link = "loge", earg=list())
link |
Link function applied to the (positive) shape parameter.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
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.
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 multivariate (matrix) response.
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
gamma2.ab
to estimate it too.
T. W. Yee
Most standard texts on statistical distributions describe the 1-parameter gamma distribution, e.g.,
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
gamma2.ab
for the 2-parameter gamma distribution,
lgammaff
.
y = rgamma(n=100, shape= exp(3)) fit = vglm(y ~ 1, gamma1, trace=TRUE, crit="c") coef(fit, matrix=TRUE) Coef(fit) summary(fit)