Re: How to find the likelihood functions?
- From: Jack Tomsky <jtomsky@xxxxxxxxxxxxx>
- Date: Tue, 28 Aug 2007 21:40:32 EDT
Hi, I am writing a winBUGS code and I need to specify
the likelihood
for the gamma distribution and I am specifying it as
the pdf:
(pow(b,a)/(exp(loggam(a)))*(exp(-b*lambda[i]))*pow(lam
bda[i],(a-1)))
But it is not accepting it although I know that I
could use the pdf in
R to estimate the parameters by MLE. There must be a
shorter form that
is the real likelihood function, (I know that for the
normal
distribution the likelihood is much shorter than the
pdf and it is
accepted by winBUGS).
Is there like a webpage where the likelihood
functions are displayed?
PS: I know that BUGS has a dgamma function and that I
do not need to
specify the likelihood function, but it is for some
other purpose I am
doing that so that I can afterwards generate a new
distribution which
is a mixture of two gamma distributions.
Thanks.
If Xi ~ Gamma(k,b), i = 1, ..., N, where k is the shape parameter and a is the scale parameter, then the likelihood function of k and b is
L(k,b) = [Prod(xi)^(k-1)]*[exp(-Sum(xi)/b]/[b^(N*k)*Gamma(k)^N]
Jack
.
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- How to find the likelihood functions?
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