Actuarial Outpost Maximum Likelihood Question: Ground Up
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#1
01-23-2015, 02:13 PM
 trondogss Member SOA Join Date: Nov 2005 Location: Master Control Program Studying for GH Specialty Posts: 8,433
Maximum Likelihood Question: Ground Up

I always get confused on what Ground Up means when doing a Maximum Likelihood (MLE) question. Particularly, I worked a problem that read as such (some stuff changed for potential copyright issues:

There is a deductible of 1 and maximum covered loss of 20:
Observe the following Payments: 3, 6, 17, 19
Fit ground-up exponential distribution using MLE.
What is the mean of the fitted distribution?

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So, when I solved this problem, I took the payments, and converted it to losses (4, 7, 18, 20+). Then used the losses to find my fitted parameter.

So...why does the solution to this problem use the payments to solve for the parameter and not the losses? Thanks in advance for the help.
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Quote:
 Originally Posted by Vomik You successfully played "just the tip?" Ive always ended up losing
#2
01-23-2015, 02:26 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,095

You should get the same result if you work with losses, as long as your formulas reflect that you have no information about losses less than one. For some other distributions (not here - exponential is memoryless) you would have to work with losses.
#3
01-23-2015, 02:31 PM
 Abelian Grape Meme-ber                         Meme-ber CAS Join Date: Jul 2014 Favorite beer: Allagash Curieux Posts: 42,062

Quote:
 Originally Posted by actuary_aspire Memoryless?
http://en.wikipedia.org/wiki/Memorylessness
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Quote:
 Originally Posted by Pension.Mathematics what's your problem man?
#4
01-23-2015, 02:34 PM
 actuary_aspire Member CAS Join Date: Sep 2009 Posts: 3,979

Quote:
 Originally Posted by Abelian Grape http://en.wikipedia.org/wiki/Memorylessness
I know. I was answering the OP's question with a question, but then saw that Gandalf had a better response, so I deleted the post.

tl;dr ninja'd
#5
01-23-2015, 02:36 PM
 Abelian Grape Meme-ber                         Meme-ber CAS Join Date: Jul 2014 Favorite beer: Allagash Curieux Posts: 42,062

i ninja'd you before you can undo gandalf ninja-ing you
__________________
Quote:
 Originally Posted by Pension.Mathematics what's your problem man?
#6
01-23-2015, 03:06 PM
 actuary_aspire Member CAS Join Date: Sep 2009 Posts: 3,979

Quote:
 Originally Posted by Abelian Grape i ninja'd you before you can undo gandalf ninja-ing you
right place at the right time.

also known as ninja.
#7
01-23-2015, 03:49 PM
 trondogss Member SOA Join Date: Nov 2005 Location: Master Control Program Studying for GH Specialty Posts: 8,433

Quote:
 Originally Posted by Gandalf You should get the same result if you work with losses, as long as your formulas reflect that you have no information about losses less than one. For some other distributions (not here - exponential is memoryless) you would have to work with losses.
great thanks, I forgot to divide by S(1).
__________________
P FM MFE MLC Modules 1-8 IA FA C ASA GH Core GH Advanced FSA Modules 2/3
Quote:
 Originally Posted by Vomik You successfully played "just the tip?" Ive always ended up losing
#8
01-23-2015, 06:16 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,707

You really need to know that the amount paid per positive payment when there is only a deductible and the ground-up loss is Exponential is itself an Exponential with the same mean as the ground-up loss. Thus, just considering the amount per payment with the deductible, you observed values of 3, 6, 17, and 19+. But for an Exponential this makes the MLE equal (3 + 6 + 17 + 19) / 3 = 15. You're done.

Jim Daniel
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