IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v133y2017icp223-234.html
   My bibliography  Save this article

On the approximation of the step function by some sigmoid functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415002554
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2015.11.005?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    2. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    3. Robert King & Irene Lena Hudson & Muhammad Shuaib Khan, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 183-210, June.
    4. Muhammad Shuaib Khan & Robert King & Irene Lena Hudson, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 183-210, June.
    5. Ahmad Alzaghal & Duha Hamed, 2019. "New Families of Generalized Lomax Distributions: Properties and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-51, November.
    6. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    7. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    8. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    9. Alya Al Mutairi & Muhammad Z. Arshad, 2022. "A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(2), pages 1-29, March.
    10. Patrick Osatohanmwen & Eferhonore Efe-Eyefia & Francis O. Oyegue & Joseph E. Osemwenkhae & Sunday M. Ogbonmwan & Benson A. Afere, 2022. "The Exponentiated Gumbel–Weibull {Logistic} Distribution with Application to Nigeria’s COVID-19 Infections Data," Annals of Data Science, Springer, vol. 9(5), pages 909-943, October.
    11. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.08343, arXiv.org.
    12. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    13. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    14. Sanaa Al-Marzouki & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2019. "Type II Topp Leone Power Lomax Distribution with Applications," Mathematics, MDPI, vol. 8(1), pages 1-26, December.
    15. Abdulaziz S. Alghamdi & M. M. Abd El-Raouf, 2023. "Exploring the Dynamics of COVID-19 with a Novel Family of Models," Mathematics, MDPI, vol. 11(7), pages 1-29, March.
    16. Jones, M.C., 2018. "Families of complementary distributions," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 74-81.
    17. Holly Brannelly & Andrea Macrina & Gareth W. Peters, 2021. "Stochastic measure distortions induced by quantile processes for risk quantification and valuation," Papers 2201.02045, arXiv.org.
    18. M. Elgarhy & Muhammad Ahsan ul Haq & Qurat Ain, 2018. "Exponentiated Generalized Kumaraswamy Distribution with Applications," Annals of Data Science, Springer, vol. 5(2), pages 273-292, June.
    19. Phillip Oluwatobi Awodutire & Oluwafemi Samson Balogun & Akintayo Kehinde Olapade & Ethelbert Chinaka Nduka, 2021. "The modified beta transmuted family of distributions with applications using the exponential distribution," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-25, November.
    20. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.

    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:eee:matcom:v:133:y:2017:i:c:p:223-234. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.