Hello, I found this forum and hoped I would be able to get help with a problem that is just consuming all of my time.
It involves finding the Maximum Likelihood Estimator. I apologize in advance for maybe not expressing any formulas correctly on here...I've never typed these in a post like this before so I don't know how to correctly type symbols for "sum" and "product" etc.
Basically, the problem is this:
Density function f(x) = (3/lambda) * x^2 * e^((-x^3)/lambda)
Find the MLE of Lambda for a random sample of size n.
So...
I began by taking the product of the function of lambda for all values of x
L(lambda, x1...xn) = (the product sign of i=1 to n) * f(xi, lambda) = (3/lambda) * x^2 * e^((-x^3)/lambda)
=> I take the derivative with respect to lambda...
dln (3/lambda^n * sum of i to n for xi^2 * e^((sum of i to n of -x^3)/(lambda^n)))
This is where I've either gone very wrong or I've just confused myself to no end.
I think you have to take the natural log with respect to lambda and solve for lambda, but the more I look at this problem and how I'm going about it the more I confuse myself.
If anyone could tell me how I could type this cleaner and look more like an actual problem on paper (with correct symbols, etc) I would be more than happy to go further, but this is basically where I'm stuck.
Any help is greatly appreciated.
Edit*
I forgot to add the parameters
x > 0 and lambda > 0
Last edited by Sublime440; 10-10-2016 at 10:27 PM. Reason: forgot to add parameters
Tweet |