<P ALIGN=RIGHT><FONT SIZE=+4>52</FONT><P>
Numerical computation of non-linear stable regression
Clyde D. Hardin Jr.
Murad S. Taqqu
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.