Actuarial Outpost Negative bimomial
 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

 DW SimpsonActuarial JobsVisit our site for the most up to date jobs for actuaries. Actuarial Salary SurveysProperty & Casualty, Health, Life, Pension and Non-Tradtional Jobs. Actuarial Meeting ScheduleBrowse this year's meetings and which recruiters will attend. Contact DW SimpsonHave a question? Let's talk. You'll be glad you did.

 Short-Term Actuarial Math Old Exam C Forum

 Thread Tools Search this Thread Display Modes
#1
02-12-2019, 11:22 AM
 smarterthancandee Member Non-Actuary Join Date: Aug 2015 Location: Harrisburg, Pennsylvania Studying for MFE College: BU Alumna Favorite beer: Butterbeer Posts: 43
Negative bimomial

Regarding the formulas in the appendix from the Loss Models book, for the negative binomial, the two parameters they give are r and B. I assume that r is the number of successes. They give E(N)=r*B and Var(N)= r*B*(1+B). Does anyone know if B is 1/prob of success & N is the number of trials to get r successes or if they are something else?
__________________

P FM MFE STAM LTAM SRM PA
VEE: Mathematical Statistics, Economics, Accounting & Finance
#2
02-12-2019, 11:36 AM
 terencechow Member SOA Join Date: Aug 2012 College: Drake University Alumni Posts: 34

The probability of success is 1 / (1 + B).
N is the number of failures before r successes, i.e. N starts from 0.
__________________
Terence Chow, ASA, CFA
Product Manager, Actuarial
coachingactuaries.com
#3
02-12-2019, 11:50 AM
 smarterthancandee Member Non-Actuary Join Date: Aug 2015 Location: Harrisburg, Pennsylvania Studying for MFE College: BU Alumna Favorite beer: Butterbeer Posts: 43

Thanks!
__________________

P FM MFE STAM LTAM SRM PA
VEE: Mathematical Statistics, Economics, Accounting & Finance
#4
02-12-2019, 05:46 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,716

Quote:
 Originally Posted by smarterthancandee Regarding the formulas in the appendix from the Loss Models book, for the negative binomial, the two parameters they give are r and B. I assume that r is the number of successes. They give E(N)=r*B and Var(N)= r*B*(1+B). Does anyone know if B is 1/prob of success & N is the number of trials to get r successes or if they are something else?
You need to be a little careful with this interpretation, since r need not be a whole number. It's OK to roughly thing of it as Terence described, but don't get flustered if you have r=2.3 or some such.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
#5
02-12-2019, 06:01 PM
 Ginerv30 SOA Join Date: Jun 2013 College: Florida State University Posts: 15

Maybe if you were taking the old C exam, you would need to get down to this level of detail for the Neg. Binomial...But since it changed to STAM, dont get boggled down in the details of the frequency distributions.

All you need to really know is their means and variances. Also maybe know which parameters are changed by adding independent random variables or which parameter is "thinned" when you want only losses greater than a certain number.
__________________
P FM MFE STAM LTAM

 Thread Tools Search this Thread Search this Thread: Advanced Search 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 08:27 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