Demon Mark II: Extremal Equations Solution & Approximation

This paper develops a new method for the solution of DEMON-type functional equations. It is shown how the latter can be reduced to solution of a separated system of simpler equations which, for discrete distributions, can be solved by linear programming methods. The reduction also permits general characteristics of the solutions to be inferred. Additionally, methods of approximation and bounding are developed and interpreted for the general case.

Because of the importance accorded to log-normal distributions for the new-product marketing problem, further details and developments are undertaken with reference to this class of distributions and then illustrated by reference to the single-parameter case.