Actuarial Outpost SOA practice problems, Question 44
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#1
01-03-2018, 11:23 AM
 colt484 SOA Join Date: Aug 2014 Posts: 14
SOA practice problems, Question 44

You are given:
(i) Losses follow an exponential distribution with mean (Theta.)
(ii) A random sample of 20 losses is distributed as follows:
Loss Range Frequency
[0, 1000] 7
(1000, 2000] 6
(2000, (Infinity) 7
Calculate the maximum likelihood estimate of (Theta.)

When I work this out, I get Theta = -1000ln(20/33). Looking at the solutions for the SOA this is the same answer, however, I evaluate this at 500. This is not listed as the correct answer and is way outside the range of possible answers. Have I missed the mark here?
#2
01-03-2018, 11:40 AM
 daaaave David Revelle Join Date: Feb 2006 Posts: 2,968

I don't have the current SOA solutions handy, but the answer is -1000/ln(20/33), not -1000*ln(20/33).
__________________

#3
01-03-2018, 11:55 AM
 colt484 SOA Join Date: Aug 2014 Posts: 14

Quote:
 Originally Posted by daaaave I don't have the current SOA solutions handy, but the answer is -1000/ln(20/33), not -1000*ln(20/33).
Algebra Mistake. Thank you.