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 peng's likelihood example but
using the gamma instead of the normal.
I get estimates back but i separately found that the analytical mle of
the scale is equal to 1/ analytical mle(shape).
and my estimates aren't consistent with that fact ? this leads me to
assume that my estimates are not correct.
can anyone tell me what i'm doing wrong. maybe my starting values are
too far off ? thanks.
make.negloglik <- function(data, fixed=c(FALSE,FALSE)) {
op <- fixed
function(p) {
op[!fixed] <- p
shape <- exp(op[1])
scale <- exp(op[2])
a <- length(data)*shape*log(scale)
b <- (shape-1)*sum(log(data))
c <- -1.0*scale*sum(data)
-(a + b + c)
}
}
vsamples<- c(14.7, 18.8, 14, 15.9, 9.7, 12.8)
nLL <- make.negloglik(vsamples)
temp <- optim(c(scale=1,shape=1), nLL, method="BFGS")[["par"]]
estimates <- log(temp)
print(estimates)
check <- estimates[1]/mean(vsamples)
print(check)
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