Let be a random sample from an exponential distribution with mean . Show that the likelihood ratio test of against has a critical region of the form or . How would you modify this so that chi-square tables could be easily used?

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- Oct 5th 2009, 09:52 PMpanda*Hypothesis Testing
Let be a random sample from an exponential distribution with mean . Show that the likelihood ratio test of against has a critical region of the form or . How would you modify this so that chi-square tables could be easily used?

- Oct 6th 2009, 08:16 AMmatheagle
The sum of indep EXP(theta's) is a

Call this sum of X_i's X and now transform to the chi square

A

So do some calculus one with the substitution