Define your SAS dataset by:
LLi be the log likelihood function with the ith observation (or size of
loss group).
Sqrt(-LLi) be the non-linear model prediction for the ith observation.
Zero (=0) be the ith "observed value"
Then use Proc NLIN to find the parameters that minimize:
Sum over i of [Sqrt(-LLi) - Zero]^2
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
----------
From: Snaps99999@aol.com [SMTP:Snaps99999@aol.com]
Sent: Monday, September 14, 1998 10:06 PM
To: casnet@lists.casact.org
Subject: Klugman's FIT procedure
To CASNET:
I'm looking for advice regarding maximum likelihood estimation
with regard to
a pricing project. Klugman's FIT procedure is currently being
used to find
the parameters of the lognormal distribution that best matches
the actual loss
distribution. It uses a maximum likelihood technique to
determine the best
fit.
However, it would be convenient if I could find a method of
performing a
maximum likelihood estimate using SAS. Is anyone aware of a
means of
performing a maximum likelihood estimate for a lognormal
distribution using an
existing SAS procedure?
As an alternative, I've found that I can develop a least squares
estimate for
the lognormal parameters using the non-linear curve fitting
procedure in SAS,
PROC NLIN. This raises several questions:
- Is there a reason to prefer the maximum likelihood estimate
over the least
squares estimate?
- Are there reasons why I should not use the least squares
estimate?
- Under what circumstances are the two methods equivalent?
- How close will the estimated parameters be for the two
methods?
Frank Schnapp
Visit the CAS Web Site at http://www.casact.org
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