Biomath (Aug 2018)

Some properties of the Blumberg's hyper-log-logistic curve

  • Roumen Anguelov,
  • Nikolay Kyurkchiev,
  • Svetoslav Markov

DOI
https://doi.org/10.11145/j.biomath.2018.07.317
Journal volume & issue
Vol. 7, no. 1

Abstract

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The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.