×

The evaluation of integrals of the form \(\int_{- \infty}^{+\infty}f[t]\exp [-t^ 2]dt:\) Application to logistic-normal models. (English) Zbl 0716.65137

The authors have in mind a situation where f(t) is an analytic function, preferably holomorphic, available in analytic form, and the locations of its poles and their residues are readily calculable. Emulating a standard analytic approach using Cauchy’s residue theorem, they obtain a form of the trapezoidal rule quadrature error which involves contour integrals and residues of f(t) in the complex plane. This approach is not new, but the authors fulfill a useful service by illustrating how to choose parameters and handle the inequalities in specific cases that arise in statistical calculations.
While the authors’ comparisons with the 20-point Gauss-Hermite rules are certainly in order, the reader should make his own decision as to which of two equally respectable alternatives to use. Much more powerful Gaussian rules are nowadays readily available, but there are advantages in using the authors’ method for its own convenience, even when a Gaussian rule seems to be more cost effective in terms of function values.
Reviewer: J.N.Lyness

MSC:

65C99 Probabilistic methods, stochastic differential equations
65D32 Numerical quadrature and cubature formulas
62E17 Approximations to statistical distributions (nonasymptotic)
41A55 Approximate quadratures

Software:

goodwin.f77
PDFBibTeX XMLCite
Full Text: DOI