IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v36y1989i4p389-397.html
   My bibliography  Save this article

Chebyshev subinterval polynomial approximations for continuous distribution functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198908)36:43.0.CO;2-S
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198908)36:43.0.CO;2-S?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arturo Fernandez, 2005. "Progressively censored variables sampling plans for two-parameter exponential distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(8), pages 823-829.
    2. Fernandez, Arturo J., 2006. "Bayesian estimation based on trimmed samples from Pareto populations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1119-1130, November.
    3. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.
    4. Weilong Fu & Ali Hirsa, 2022. "Solving barrier options under stochastic volatility using deep learning," Papers 2207.00524, arXiv.org.
    5. Edirisinghe, Chanaka & Atkins, Derek, 2017. "Lower bounding inventory allocations for risk pooling in two-echelon supply chains," International Journal of Production Economics, Elsevier, vol. 187(C), pages 159-167.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:36:y:1989:i:4:p:389-397. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.