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#1
02-21-2007, 06:54 PM
 dmw Member Join Date: Mar 2005 Posts: 345
Mahler Likelihood Ratio Test question

This question is from Mahler's guide to Fitting Loss Distributions, 2007, section 13, Likelihood Ratio Test.

In question 13.14:

You are given the following 5 claims: 40, 150, 230, 400, 770.
You assume the size of loss distribution is Gamma.

Determine the result of using the likelihood ratio test in order to test the hypothesis that alpha = 3 and theta = 200 versus the alternative, alpha = 3.

A. Reject at the .005 sig. level
B. Reject at the .010 sig. level, but not at the .005 sig. level
C. Reject at the .025 sig. level, but not at the .010 sig. level
D. Reject at the .050 sig. level, but not at the .025 sig. level
E. Do not reject at the .050 sig. level

The answer is D. The number of degrees of freedom used to solve this question is 1 = 1 - 0

My questions are: Which hypothesis has 1 parameter. , which hypothesis has 0 parameters and why for each one? I thought that H0 would have 2 params. and H1 would have 1 param. But, that goes against the rules of the Likelihood Ratio Test, which, according to Mahler is: "H0 is the hypothesis that the distribution with fewer parameters is appropriate. The alternative hypothesis H1 is that the distribution with more parameters is appropriate."

Thanks.
#2
02-21-2007, 07:01 PM
 YoungestEverFSA Member Join Date: Oct 2006 Posts: 178

I think the likelyhood ration test tests whether finding a parameter from the data (which should be closer and therefore fit the data better than an arbitary figure), makes a SIGNIFICANT difference.

In this case, in the example where you are given both alpha and theta, you are not estimating any parametres FROM THE DATA, and therefore the number of estimated parameters is 0. In the second case, you are estimating only theta FROM THE DATA, and therefore the number of estimated parametres is 1.
#3
02-22-2007, 01:38 PM
 Howard Mahler Member CAS Join Date: May 2002 Location: Boston, MA Posts: 1,491

Youngest is exactly correct.

Come back in a week and try either 13.21 (4,11/03, Q.28) , 13.22 (4, 11/05, Q.25), or 13.8 to 13.11.

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