Actuarial Outpost MLE question involving both frequency and severity distributions
 User Name Remember Me? Password
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Enter your email to subscribe to DW Simpson weekly actuarial job updates. li.signup { display: block; text-align: center; text-size: .8; padding: 0px; margin: 8px; float: left; } Entry Level Casualty Health Life Pension All Jobs

 Thread Tools Display Modes
#1
09-24-2017, 03:29 PM
 Seasplash Member CAS SOA Join Date: Jun 2014 Location: Arlington, VA Studying for MLC College: Cal Poly San Luis Obispo Posts: 292
MLE question involving both frequency and severity distributions

There are two claims in 1 year, and the frequency distribution is Poisson with parameter theta. Those two claims are x = 3 and x = 6 and the severity follows an Inverse exponential distribution with parameter theta. Estimate theta using MLE.

Would the answer be 8/3? I just want to make sure I'm doing it correctly. If someone can show the solution that would be great too, thanks.
__________________
P FM MFE C MLC
#2
09-25-2017, 02:30 PM
 catdynasty528 Member Join Date: Jul 2011 College: Ball State University Posts: 73

I also got 8/3.

I'm guessing your solution is correct if you want to post it and the community can verify.
#3
09-25-2017, 03:00 PM
 ALivelySedative Member CAS Join Date: Dec 2013 Location: Land of the Pine College: UNC-Chapel Hill Alum Favorite beer: Red Oak Posts: 1,872

How bad is it that I already don't remember how to do this off the top of my head...??
__________________
1/P | 2/FM | 3F/MFE | LC | ST |4/C | 5 | 6 || 7 | 8 | 9
VEE: Econ, Fin, Stat
OC1, OC2
COP
#4
09-25-2017, 09:29 PM
 Milton Friedman CAS Join Date: Mar 2015 College: JMU Posts: 12

that's the answer I got as well-I suppose that's right.
#5
09-25-2017, 10:01 PM
 Seasplash Member CAS SOA Join Date: Jun 2014 Location: Arlington, VA Studying for MLC College: Cal Poly San Luis Obispo Posts: 292

Alright thanks! Just needed the confirmation!
__________________
P FM MFE C MLC
#6
12-06-2017, 09:16 AM
 Bash Member SOA Join Date: Jun 2010 Posts: 57

Can someone please post the solution. I don't know why I'm getting 4/3 and not 8/3 as gotten by everybody.
__________________
P FM MFE C MLC
VEE: Statistics Corporate Finance Economics
#7
12-06-2017, 09:42 AM
 daaaave David Revelle Join Date: Feb 2006 Posts: 2,941

$L(\theta) = \Pr[N=2] \cdot f(3 \mid \theta) \cdot f(6 \mid \theta) = e^{-\theta} \cdot \frac{\theta^2}{2} \cdot \frac{\theta e^{-\theta/3}}{9} \cdot \frac{\theta e^{-\theta/6}}{36} = c \theta^4 e^{-3\theta/2}$
$\ell(\theta) = \ln(c) + 4 \ln(\theta) - \frac{3\theta}{2}$
$\ell^\prime(\theta) = 0 + \frac{4}{\theta} - \frac{3}{2}$
and solving gives theta-hat = 8/3
__________________

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 02:13 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top

Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.29613 seconds with 11 queries