Hybrid Zipf-Mandelbrot law

There is a unified approach, maximization of Shannon entropy, that naturally follows the path of generalization from Zipf's to hybrid Zipf's law. Extending this idea we make transition from Zipf-Mandelbrot to hybrid Zipf-Mandelbrot law. It is interesting that examination of its densities provides some new insights of Lerch's transcendent. © ELEMENT, Zagreb.

Authors
Jakšetić J.1 , Pečarić D.2 , Pečarić J. 3, 4
Journal
Journal of Mathematical Inequalities
Publisher
Element D.O.O.
Number of issue
1
Language
English
Pages
275-286
Status
Published
Link
External link
DOI
10.7153/JMI-2019-13-20
Volume
13
Year
2019
Organizations
  • 1 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, Zagreb, 10000, Croatia
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
  • 3 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
  • 4 RUDN University, Miklukho-Maklaya str.6, Moscow, 117198, Russian Federation
Keywords
Chebyshev's inequality; Lerch's transcendent; Log-convex functions; Lyapunov's inequality; Shannon entropy; Zipf-Mandelbrot law
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