Question on ASM 30.13

Here is the question. The following are 10 ground up losses observed in 1999:

18, 78, 125, 168, 250, 313, 410, 540, 677, 1100. You are given:



1) The sum of the 10 losses equals 3679.

2) Losses are modeled using an exponential distribution with Maximum Likelihood estimation.

3) 5% inflation is expected in 2000 and 2001

4) All policies written in 2001 have d=100 and u =100. (The max payment per loss is 900)

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I understand the given solution. I would like to know what is wrong with the approach that I took to find theta-hat. Here is what I did:



1) Multiply all losses by 1.05^2 for inflation. Losses are now 19.85, 86, 137.81, 185.22, 275.63, 345.08, 452.03, 595.35, 746.39, 1212.75.



2) Apply deductible and policy limit to losses. Payments are now:

0, 0, 37.81, 85.22, 175.63, 245.08, 352.03, 495.35, 646.39, 900.



3) Use exponential MLE shortcut for Theta-hat(Total pmts/ #uncensored data pts.)

Theta-hat = 2937.51/7 =419.64.



(Theta-hat is supposed to be 405.61)



What did I do wrong? Thanks so much!

Question on ASM 30.13