So I have a Weibull Distribution with two parameters with the following pdf:
If I know , how can I find the sufficient statistic for ? I believe (correct me if I am wrong, I can use either the Neyman Factorization theorem or express the pdf in an exponential family?)
Have no idea how to add spaces in math code..
Last edited by MegaMan; 12-02-2011 at 01:30 PM.
I have a hunch that expressing it in exponential family form would probably be the easiest way to do it in this case. But that's just a hunch. I know if both parameters are unknown then I don't think we can do better than the set of order statistics. But if we know it looks like things would be a little bit nicer.
When I am simplifying it, do I need to group up certain parts? i.e. do I need to seperate alpha from beta
Last edited by MegaMan; 12-02-2011 at 03:17 PM.
Not sure what hint can be given because that is "straight forward" in the sense that it just require you to group the terms appropriately.
What have you try? via Exponential family/factorization theorem?
Beta is treated as a constant like 1, 2, 3. So do not worry about that.
The first and the second term has mistake. Please try again.
Yes he is sure. So am I. Note that x^2 + y^2 is not the same as (x+y)^2. And also be a little more careful with your log rules.
And in the middle part, outside the exponential, how can you have a summation when you are actually having a product of marginal pdfs?
Last edited by MegaMan; 12-02-2011 at 06:30 PM.
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