A language for numerical construction of applied stochastic models via redundant data

Abstract

AbstractA language is described for rapid implementation of algebraic operations on random variables that can be used for numerical construction of stochastic models. A “data object” describing the probability distribution function of a random variable may consist of mutually redundant data‐sets such as: a sampling of its probability distribution function, coefficients of the moment generator function, fast Fourier transform of a sampling of the probability density function, a set of bilateral PHase (BPH) coefficients, fast Fourier transform of a set of BPH coefficients, a set of Laguerre transform coefficients, and other representations. We exploit this redundancy of data representations in implementing our language and in obtaining a computational speed‐up for random variable manipulations. If X and Y are two random variables, the operation of addition to evaluate X + Y is implemented in a simple high‐level language construct “+”. The language is also provided with the capability of easily supporting other user‐defined algebraic operations for random variables. This language (RANL) is a powerful computational tool that can be used to build complex and realistic numerical stochastic models rapidly. The operators used in RANL for manipulation of random variables are extensions of arithmetic operators for real numbers.