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Summary: Supplementary notes for new Part IIC course:
Statistical Modelling, using the gamma
distribution
P.M.E.Altham
January 4, 2005
We follow the notation of McCullagh and Nelder (1970), who de ne the
density function of the gamma distribution with mean and shape parameter
as
f(yj; ) = 1
() (y=) e y= 1
y
for y > 0:
You may check that this gives
E(Y ) = ; var(Y ) = ( 2 )=;
and the density is of standard glm form with = 1=, and canonical link
= 1=.
We simulate from two gamma distributions below, and use the glm tting pro-
cedure, with canonical link (ie the inverse). See if you can work out what's
going on.
> library(MASS)
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