Numerical computation of non-linear stable regression functions

Abstract

A previous paper by the authors gives explicit formulas for the regression function of one stable random variable upon another. Although the regression may sometimes be linear, it is in general not a linear function. It involves the quotient of two integrals which cannot be computed analytically and must therefore be approximated numerically. Although the general problem of computing the integrals is straightforward in principle, the specific task is fraught with difficulties. In order to allow the practioner to apply the formulas, this paper presents a self-contained exposition of the regression problem and a software package, written in the C language, which overcomes the numerical difficulties and allows the user control over the accuracy of the approximation. The package also allows the user to compute numerically the probability density function of a stable random variable.

The last two authors were supported by the AFOSR grant 89–0115 and the ONR grant 90-J-1287 at Boston University.