maximum likelyhooh estimator

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

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.

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)