Appendix D
The Recursive Formula
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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