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On the approximation of the step function by some sigmoid functions

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  • Iliev, A.
  • Kyurkchiev, N.
  • Markov, S.

Abstract

In this note the Hausdorff approximation of the Heaviside step function by several sigmoid functions (log–logistic, transmuted log–logistic and generalized logistic functions) is considered and precise upper and lower bounds for the Hausdorff distance are obtained. Numerical examples, that illustrate our results are given, too.

Suggested Citation

  • Iliev, A. & Kyurkchiev, N. & Markov, S., 2017. "On the approximation of the step function by some sigmoid functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 223-234.
    • Handle: RePEc:eee:matcom:v:133:y:2017:i:c:p:223-234
    DOI: 10.1016/j.matcom.2015.11.005
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    References listed on IDEAS

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    1. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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    Cited by:

    1. Xuehu Yan & Feng Liu & Wei Qi Yan & Yuliang Lu, 2020. "Applying Visual Cryptography to Enhance Text Captchas," Mathematics, MDPI, vol. 8(3), pages 1-13, March.

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