find likelihood ratio test and the power function

**szpengchao** · February 23rd 2009, 12:04 AM

$X_{1},...,X_{n}$ are identically exponentially distributed.

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

find the expression for the power function.

**WeeG** · February 23rd 2009, 01:57 AM

can't give you the whole solution, but this might help:

**matheagle** · February 23rd 2009, 04:41 PM

BE very careful here.
When you say gamma or exponential you NEED to be more precise.
DO you mean...
${e^{-x/\theta}\over \theta}$
or...
$\theta e^{-x\theta}$
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.

**WeeG** · February 23rd 2009, 11:27 PM

you are right...!

**matheagle** · February 24th 2009, 07:11 AM

eye no

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