What it boils down to is that if the Number of claims N is a random
variable with a Poisson distribution and mean and variance both equal to
n, and if the size of a claim is another random variable X (and N and X
are independent)
then the formula for the variance of C = X1 + X2 +....Xn is:
Var (C) = E[N] * Var (X) + Var (N) * E[X]^2
Var (C) = n*s^2 + n*m
where m is the mean of the size of the claim and s^2 is the variance of
the size of the claim distribution.
John Nauss
johnau@safeco.com
-----Original Message-----
From: Dimitra Roidakis [SMTP:dr@g-g-a.com]
Sent: Friday, August 21, 1998 9:22 AM
To: studygroup4b@lists.casact.org
Subject: Hossak Pollard Zehnwirth
I have a question concerning Full Credibility theory, page 157 of
HPZ. When they state that Var(C)=n(s^2+m^2)
To me Var(C)=Var(X1+X2+...Xn)=Var(X1)+..Var(Xn)=nS^2
(were S^2 stands for sigma square)
My question is where does the nm^2 comes from?
Dimitra
dr@g-g-a.com