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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7.4 Effect of exposure on frequency
Assume that the current portfolio consists of n entities, each of which could produce claims. Let Nj be the number of claims produced by the jth entity. Then N = N1 + ··· + Nn. If we assume that the Njs are independent and identically distributed, then
Now suppose the portfolio is expected to expand to n* entities with frequency N*. Then
Thus, if N is infinitely divisible, the distribution of N* will have the same form as that of N, but with modified parameters.
EXAMPLE 7.18
It has been determined from past studies that the number of workers compensation claims for a group of 300 employees in a certain occupation class has the negative binomial distribution with β = 0.3 and r = 10. Determine the frequency distribution for a group of 500 such individuals.
The pgf of N* is
which is negative binomial with β = 0.3 and r = 16.67.
For the (a, b, 0) class, all members except the binomial have this property. For the (a, b, 1) class, none of the members do. For compound distributions, it is the primary distribution that must be infinitely divisible. In ...
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