# Maxiumum Likelihood function

• Jan 17th 2010, 03:05 PM
scubasteve123
Maxiumum Likelihood function
observations 1,2,...n are made from a distribution with the following pdf:
f(x)=theta/x^(theta+1)

find an expression for theta hat.
• Jan 17th 2010, 05:49 PM
theodds
Starting from the definition of the liklihood function, you end up with $\frac{\theta ^ n}{\prod _{i = 1} ^ n x_i ^ {\theta + 1}}$. From there, the trick should be to maximize the log of this guy, which is a pretty standard thing to do. In most cases, maximizing a function is equivalent to maximizing its log. I ended up with $\hat{\theta} = \frac{n}{\sum _ {i = 1} ^ n \mbox{log}(x_i)}$ if I did it right.
• Jan 18th 2010, 01:06 AM
mr fantastic
Quote:

Originally Posted by scubasteve123
observations 1,2,...n are made from a distribution with the following pdf:
f(x)=theta/x^(theta+1)

find an expression for theta hat.

You will find several examples in this subforum of how to find a maximum likelihood estimate. I suggest you find them (use the Search tool) and review them.