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#1




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 groundup exponential distribution using MLE. What is the mean of the fitted distribution? ____________________________ 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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#2




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




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#8




You really need to know that the amount paid per positive payment when there is only a deductible and the groundup loss is Exponential is itself an Exponential with the same mean as the groundup 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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Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
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