find likelihood ratio test and the power function

• Feb 23rd 2009, 12:04 AM
szpengchao
find likelihood ratio test and the power function
$\displaystyle X_{1},...,X_{n}$ are identically exponentially distributed.

find the likelihood ratio test of size alpha of $\displaystyle H_{0}:\theta=\theta_{0}, \ \ \ H_{1}:\theta=\theta_{1}>\theta_{0}$

find the expression for the power function.
• Feb 23rd 2009, 01:57 AM
WeeG
can't give you the whole solution, but this might help:
• Feb 23rd 2009, 04:41 PM
matheagle
BE very careful here.
When you say gamma or exponential you NEED to be more precise.
DO you mean...
$\displaystyle {e^{-x/\theta}\over \theta}$
or...
$\displaystyle \theta e^{-x\theta}$
Most people use the first one.
BUT the solution just posted used the second.
HENCE the answers to these two are either the sample mean
or the reciprocal of the sample mean, since one theta is the reciprocal of the other.
• Feb 23rd 2009, 11:27 PM
WeeG
you are right...!
• Feb 24th 2009, 07:11 AM
matheagle
eye no