September 2012
Beginner to intermediate
536 pages
14h 40m
English
book
Loss Models: From Data to Decisions, 4th Edition
by Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot
Content preview from Loss Models: From Data to Decisions, 4th Edition
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19.3 Semi parametric estimation
In some situations it may be reasonable to assume a parametric form for the conditional distribution 
. The situation at hand may suggest that such an assumption is reasonable or prior information may imply its appropriateness.
For example, in dealing with numbers of claims, it may be reasonable to assume that the number of claims mij Xij for policyholder i in year j is Poisson distributed with mean mijθi given 
i = θi. Thus E(mijXij|i) = Var(mijXij|i) = miji, implying that μ(i) = v(i) = i, and so μ = v in this case. Rather than use (19.13) to estimate v, we could use to estimate v.
EXAMPLE 19.6
In the past year, the distribution of automobile insurance policyholders ...
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