maximum likelyhooh estimator

[Juriaan Borst]

Does anyone know how to calculate the maximum likelyhood estimator of e^(2m+2s^2) of for a normal distribution (m,s^2)

where m = mu and s = sigma


Hope someone can help

[Illuminator]

This isn't my prefered area of math but here goes.

the likelihood function is

lik(m, s) = f(xi | m, s)
or
lik(m, s) = f(X1 | m,s) * f(X2 | m,s)*...* f(Xn | m,s)

Your first want the find the Log Likelihood

l(m, s) = Summation of Log[f(Xi | m, s)] for i= 1 to n

then to find the maximum likelihood estimator for your standard deviation (s) and mean (m) you take the partial derivative with respect to these varaibles.

for a normal distribution these values are
m = X
and
s = sqrt(1/n*Summation of (Xi - X)^2 for i= 1 to n)

since your function is not exactly the normal distribution function your answers will be slightyly different different.

[jim mcnamara]

Illuminator's answer was great, but it's possible that it may not be exactly what you need, There are in fact, a lot of methods. Or it ain't simple.

Here is a page with a lot of different algotihms for likelihood estimators. Pick one that fits (they're in FORTRAN, oops)