Actuarial Outpost Negative bimomial
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 Short-Term Actuarial Math Old Exam C Forum

#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?
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#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.
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#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!
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#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: 2,711

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.
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#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.
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