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Chebyshev subinterval polynomial approximations for continuous distribution functions

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  • Hsien‐Tang Tsai
  • Herbert Moskowitz

Abstract

An algorithm for constructing a three‐subinterval approximation for any continous distribution function is presented in which the Chebyshev criterion is used, or equivalently, the maximum absolute error (MAE) is minimized. The resulting approximation of this algorithm for the standard normal distribution function provides a guideline for constructing the simple approximation formulas proposed by Shah [13]. Furthermore, the above algorithm is extended to more accurate computer applications, by constructing a four‐polynomial approximation for a distribution function. The resulting approximation for the standard normal distribution function is at least as accurate as, faster, and more efficient than the six‐polynomial approximation proposed by Milton and Hotchkiss [11] and modified by Milton [10].

Suggested Citation

  • Hsien‐Tang Tsai & Herbert Moskowitz, 1989. "Chebyshev subinterval polynomial approximations for continuous distribution functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 389-397, August.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:4:p:389-397
    DOI: 10.1002/1520-6750(198908)36:43.0.CO;2-S
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    References listed on IDEAS

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    1. E. Page, 1977. "Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 75-76, March.
    2. Hugo C. Hamaker, 1978. "Approximating the Cumulative Normal Distribution and its Inverse," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(1), pages 76-77, March.
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