parameter estimation by MLE method

[Ferra]

Hi All

I need to estimate two unknown parameters (lambda1 and lambda2) by using MLE. I know that they have normal distribution. h = g(lambda1 , lambda2) where h is random variable. how can I do it?
I thought I should write: f(h) = Jacobian * Nor(mu1 , sigma1)*Nor(mu2 , sigma2)
Also I thought about hierarchical Bayesian method too...

Thanks in advance

 

[Ferra]

Actually h is a function of these two parameters and we don't know the distribution of h but we know than the two parameters are distributed normally. So we want to estimate these two parameters..

 

[BGM]

I think you need to clarify your question. If you want to find the MLE, at least you need to provide the likelihood function, as a function of the parameters \( \lambda_1, \lambda_2 \). The information you provided is quite confusing.

 

[Ferra]

Sure.
L( \lambda_1, \lambda_2 \mid h )
\lambda_1, \lambda_2 are the unknown parameters that have Normal distribution

 

[Dason]

Well if that's as helpful as you're going to be then about the best we'll be able to do is to tell you to differentiate your log likelihood function with respect to each parameter and solve the corresponding system of equations to find the MLEs.

Take a step back and look at the information you've given us. Do you really think you've provided enough information in a coherent enough manner for us to be able to provide useful help?