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.

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- Jan 17th 2010, 03:05 PMscubasteve123Maxiumum 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 PMtheodds
Starting from the definition of the liklihood function, you end up with $\displaystyle \frac{\theta ^ n}{\prod _{i = 1} ^ n x_i ^ {\theta + 1}}$. 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 $\displaystyle \hat{\theta} = \frac{n}{\sum _ {i = 1} ^ n \mbox{log}(x_i)}$ if I did it right.

- Jan 18th 2010, 01:06 AMmr fantastic