Efficient evaluation of the area under the normal curve

ABSTRACT

The task of evaluating the cumulative distribution of a normally distributed random variable is considered. A brief introduction into this problem is given and several possible approximations are presented as APL functions. Many of these functions have been written in two versions. The first version is written in the original APL style. the companion function using an APL2 coding style is also included in the paper for purposes of comparison. Both versions have been tested using simple data vectors of varying lengths and run under APL on an IBM 3090 with and without a Vector Facility. The results are compared among the algorithms, between the coding styles, and with and without hardware support for vector processing.

REFERENCES

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• Bo87b: Bogart, B., Personal communication, May, 1987.
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Error analysis

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Languages