Actuarial Outpost SOA #250
 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

 Salary Surveys Property & Casualty, Life, Health & Pension Health Actuary JobsInsurance & Consulting jobs for Students, Associates & Fellows Actuarial Recruitment Visit DW Simpson's website for more info. www.dwsimpson.com/about Casualty JobsProperty & Casualty jobs for Students, Associates & Fellows

 Short-Term Actuarial Math Old Exam C Forum

#1
05-28-2018, 10:36 AM
 ElectroSpecter Member SOA Join Date: Nov 2011 College: Going to school for axe throwing Favorite beer: Blue Point No Apologies Double IPA Posts: 182
SOA #250

(Please forgive my makeshift symbols, I'm posting this from my phone and it is cumbersome to use Latex; ¤ is theta). In the answer, we're "shown" that ¤(186^-2)exp(-¤/186)¤(91^-2)exp(-¤/91)¤(66^-2)exp(-¤/66)(exp(-¤/60))^7 is proportional to ¤^3(exp(-0.148184¤). How? I have no idea what they're doing here (and this isnt the only mle solution where they're doing this).

It's like the coefficients just go away and I'm also not sure what they're doing in the exponents.
#2
05-28-2018, 11:19 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,339

I haven't worker it out, but I assume that is the result if you add the exponents, combine the theta terms, and leave out the constant.
#3
05-28-2018, 12:59 PM
 ElectroSpecter Member SOA Join Date: Nov 2011 College: Going to school for axe throwing Favorite beer: Blue Point No Apologies Double IPA Posts: 182

Okay, yes. That's what they did. It's quite obvious in retrospect. I guess now my question is why are we allowed to drop the coefficients? Is it because they go away anyway once we take the derivative of the loglikelihood?
#4
05-28-2018, 01:25 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,004

Quote:
 Originally Posted by ElectroSpecter Okay, yes. That's what they did. It's quite obvious in retrospect. I guess now my question is why are we allowed to drop the coefficients? Is it because they go away anyway once we take the derivative of the loglikelihood?
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"

"I think that probably clarifies things pretty good by itself."
#5
05-28-2018, 06:45 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,688

Quote:
 Originally Posted by ElectroSpecter Okay, yes. That's what they did. It's quite obvious in retrospect. I guess now my question is why are we allowed to drop the coefficients? Is it because they go away anyway once we take the derivative of the loglikelihood?
It's also because maximizing 1000 (say) times f occurs at the same point as maximizing f.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
#6
05-28-2018, 06:58 PM
 ElectroSpecter Member SOA Join Date: Nov 2011 College: Going to school for axe throwing Favorite beer: Blue Point No Apologies Double IPA Posts: 182

Got it, it all makes sense now. I don't know what my problem was regarding the exponents, I think I was just adding them wrong. Sometimes when I get hyperfocused on the exam material itself, I start having issues with stuff like this that should be obvious.