Description: In a recent note Ralph Garfield brought up a problem which seems to exist in using the method of separation of symbols. In contrast with his conviction we believe that the operator relations proved by operational calculus are practically useful, of course if they are interpreted in the correct sense.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].