# [R] maximum likelihood estimation of 5 parameters

francogrex francogrex at mail.com
Fri Jan 5 13:54:50 CET 2007

```Hi Guys, it would be great if you could help me with a MLE problem in R.

I am trying to evaluate  the maximum likelihood estimates of theta = (a1,
b1, a2, b2, P) which defines a mixture of a Poisson distribution and two
gamma prior distributions (where the Poisson means have a gamma
distribution, actually 2 gammas and P is the mixing factor). The likelihood
function for theta is L(theta) = Pi,j{P f(Nij; a1, b1, Eij) + (1 – P) f(Nij;
a2, b2, Eij),}
The maximum likelihood estimate of theta is the vector that maximizes the
above equation (the values of N and E are given). The authors of the article
I read say that the maximization involves an iterative search in the five
dimensional parameter space, where each iteration involves computing
log[L(theta)] and its first and second-order derivatives. In test runs it is
suggested that the maximization typically takes between 5 and 15 iterations
from the starting point theta = (a1 = 0.2, b1 = 0.1, a2 = 2, b2 = 4, P =
1/3).

Now I have done maximization of a gamma-poisson mixture before (1 poisson, 1
gamma) successfully and I could determine correctly alpha (a) and beta(a).
But this one above is giving me ridiculously large unusable values (for
example P should not be above 1 and sometimes I get values of 500!) or even
negative values! I know the values I should be obtaining with my samples
shouldn't be far from the staring points. Is there a way to help me solve
this issue? Thanks.
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```