The purpose of this note is to develop some of the formulae of the classical theory of risk by a uniform treatment in which the “deaths’ column of the life table is considered as a discontinuous frequency distribution. The paper thus forms an example of the application of standard statistical processes to actuarial theory, and also supplies demonstrations of certain of the results quoted without proof in the survey by E. Lukacs. The aim has been to provide an elementary introduction both to an actuarial subject long neglected in this country, and to statistical methods of general utility.

The paper owes its origin to a stimulating series of talks on the Theory of Risk, given by S. Vajda to the statistical Study Group of the Society. The particular approach adopted and the treatment of composite policies are thought to be original.