A simple method for representing some univariate frequency distributions, with particular application in Monte Carlo-based simulation

Introduced in this paper is a simple yet effective method for representing some of the types of univariate frequency distribution that commonly are required in Monte Carlo-based simulation. To use the method, an appropriate parent distribution is first chosen; then this distribution is modified by blending a constant value into the density function; the particular value used is the ordinate of the density function at its mode. The advantages of the method are (1) that a wide variety of forms of distribution can be represented, (2) that the number of parameters is low, (3) that the parameters can be varied continuously to let sets of systematically related distributions be constructed, and (4) that the resulting distribution functions are straightforward to invert numerically, thereby letting random deviates be generated quickly and efficiently. The method is potentially of particular value in Monte Carlo-based simulation, because it allows distributions of greatly differing forms to be represented within a single, flexible framework. The paper describes the method, provides the necessary equations for parameter estimation, and gives an example of a simulation exercise in which the method proved valuable. A demonstration program is provided that allows experimentation with the method.