Estimates the 1-parameter gamma distribution by maximum likelihood estimation.
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Link function applied to the (positive) shape parameter.
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
The mean of Y (returned as the default fitted values)
is mu=shape, and the variance is
sigma^2 = shape.
An object of class
The object is used by modelling functions such as
This VGAM family function can handle a multiple responses, which is inputted as a matrix.
The parameter shape matches with
rgamma. The argument
rgamma is assumed
1 for this family function, so that
scale = 1 is used for calls to
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.
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