Suppose has density if otherwise

Describe how to sample from this distribution using the method of inversion.

Find the MLE estimates for and from samples.

Determine the asymptotic variance of the MLE estimates.

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- Mar 29th 2010, 06:39 PMAnonymous1Parameter estimation
Suppose has density if otherwise

Describe how to sample from this distribution using the method of inversion.

Find the MLE estimates for and from samples.

Determine the asymptotic variance of the MLE estimates. - Mar 30th 2010, 05:07 AMCaptainBlack
First find the cumulative distriution function , then find the inverse function of this:

where the domain of is [0,1) and range is

Now generate a random number and has the required distribution, and I am absolutly certain that this is in your notes and or text book.

CB - Mar 30th 2010, 11:21 AMAnonymous1
My problem is mostly with I cannot simply set to maximize. So what do I do?

- Mar 30th 2010, 08:39 PMmatheagle
Does that mean me?

The likelihood function is...

so if you want to maximize this wrt a, you want a as big as possible, since bn>0.

The largest a can be is the smallest order stat, i.e., the min.

As for the max wrt b it looks like you can take the log and differentiate. - Mar 30th 2010, 10:04 PMAnonymous1
- Mar 31st 2010, 07:35 PMAnonymous1
Sorry if this is a stupid question, but what exactly is this about?

- Mar 31st 2010, 08:40 PMmatheagle
It's an indicator function, some call it a characteristic function.

But I use that terminology for the Fourier transform.

And I combine what some people use in a subscript with the argument.

if

while if

Most people write as

I combine the subscript and the argument. - Mar 31st 2010, 08:53 PMmatheagle
If then instead of saying that f(x) is 0 otherwise, use...

and this notation makes it easier to see how the max and min are suff stats in many problems.