Negative Binomial Rationale [Discussion]

Mr. Carlson sets forth one of the reasons for writing his paper in these words: "... We are all interested in finding tools that work. But we should not be satisfied as actuaries without probing into any unfamiliar mathematical model until we know why it works, because thus only do we learn whether it is the best model for the purpose or whether is can be improved upon, and also what extensions of its utility may be available .... " For some of us the utility of a model increases to the extent that it makes possible a visual image of something physical: Gears turning other gears where there is causal linkage, or colored balls being drawn out of an urn where the problem is that of defining the particular degree of absence of causal linkage. Models that make possible visual imagery may be a handicap to the investigator while he is pursuing his investigation, but they will help him communicate his findings to a larger audience after he has found something.