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FLDS: A Flexible, Limited, Double‐Sigmoid Transmission Function.

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Title: FLDS: A Flexible, Limited, Double‐Sigmoid Transmission Function.
Authors: Rosenberger, Albert1 (AUTHOR) arosenb@gwdg.de, Malinowski, Marek T.1 (AUTHOR) malinowskimarek@poczta.fm
Source: Journal of Probability & Statistics. 3/17/2026, Vol. 2026, p1-10. 10p.
Subjects: Nonlinear functions, Mathematical functions, Curve fitting, Parameterization, Monotonic functions, Goodness-of-fit tests, Spline theory
Abstract: The values of a measured, derived or estimated variable often differ from the "true," "undistorted" values of a desired dimension. Output values of noncalibrated measuring instruments, misspecification of analysis models or too inflexible activation functions can lead to inappropriate decisions in all situations. Therefore, a highly flexible mathematical function (FLDS) for the isotonic transformation of a variable X of the value space (0‐1) to a variable Y of the same value space (0‐1) is presented here. With four or six parameters, almost all conceivable function curves can be represented. This allows overcoming restrictions of other functions, such as linearity or constant curvature. FLDS outperforms competitors such as spline functions or an adapted version of the Emax function in terms of the goodness of fit to the simulated data. The FLDS function can be used in a variety of ways. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Probability+%26+Statistics%22">Journal of Probability & Statistics</searchLink>. 3/17/2026, Vol. 2026, p1-10. 10p.
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  Data: The values of a measured, derived or estimated variable often differ from the "true," "undistorted" values of a desired dimension. Output values of noncalibrated measuring instruments, misspecification of analysis models or too inflexible activation functions can lead to inappropriate decisions in all situations. Therefore, a highly flexible mathematical function (FLDS) for the isotonic transformation of a variable X of the value space (0‐1) to a variable Y of the same value space (0‐1) is presented here. With four or six parameters, almost all conceivable function curves can be represented. This allows overcoming restrictions of other functions, such as linearity or constant curvature. FLDS outperforms competitors such as spline functions or an adapted version of the Emax function in terms of the goodness of fit to the simulated data. The FLDS function can be used in a variety of ways. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Probability & Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/jpas/6076741
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        Text: English
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      – SubjectFull: Nonlinear functions
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
      – SubjectFull: Curve fitting
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      – SubjectFull: Parameterization
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      – SubjectFull: Monotonic functions
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      – SubjectFull: Goodness-of-fit tests
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      – SubjectFull: Spline theory
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              Text: 3/17/2026
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              Y: 2026
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