The recursive formula is (where the frequency distribution is a member of the class),
where , , , and . Note that the severity distribution (X) must place probability on nonnegative integers. The formula must be initialized with the value of . These values are given in Table D.1. It should be noted that, if N is a member of the class, , and so the first term will vanish. If N is a member of the compound class, the recursion must be run twice. The first pass uses the secondary distribution for , , a, and b. The second pass uses the output from the first pass as and uses the primary distribution for , , a, and b.
Table D.1 Starting values for recursions.
Distribution | |
Poisson | |
Geometric | |
Binomial | |
Negative binomial | |
ZM Poisson | |
ZM geometric | |
ZM binomial | |
ZM negative binomial | |
ZM logarithmic |
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