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gammafun
2008 May 23
1
maximizing the gamma likelihood
for learning purposes and also to help someone, i used roger peng's
document to get the mle's of the gamma where the gamma is defined as
f(y_i) = (1/gammafunction(shape)) * (scale^shape) * (y_i^(shape-1)) *
exp(-scale*y_i)
( i'm defining the scale as lambda rather than 1/lambda. various books
define it differently ).
i found the likelihood to be n*shape*log(scale) +
(shape-1)*sum(log(y_i) - scale*sum(y_i)
then i wrote below which is just roger...