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A Bread-and-Butter Algorithm for Probability Integrals

In: Computing Science and Statistics

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  • Chaiho C. Wang

    (The George Washington University)

Abstract

This paper presents a numerical integration algorithm based on the classicRomberg’s extrapolation method. The modification allows easy handling of improper integrals or integrals with end-point singularities. This algorithm is versatile, fast, and accurate. It may eliminate for some researchers the need for carrying around tables of integrals, and housing a bundle of tailor-fit algorithms for different integrals. Running on a personal computer, implemented in single precision Fortran (and within its limitations), the algorithm produced, to six-digit accuracy, all integral related tables found in Abramowitz and Stegun, “Handbook of Mathematical Functions.” With a few exceptions of difficult integrals, it can produce a data filled table of your own in seconds.

Suggested Citation

  • Chaiho C. Wang, 1992. "A Bread-and-Butter Algorithm for Probability Integrals," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 553-556, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_99
    DOI: 10.1007/978-1-4612-2856-1_99
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