Majorizatiuon and ZipfMandelbrot law
N. Latif, Ð. Pečarić,
J. Pečarić
In this paper we show how the ZipfMandelbrot law is connected to the theory of majorization. Firstly we consider the
Csiszár fdivergence for the ZipfMandelbrot law and then develop important
majorization inequalities for these divergences. We also discuss some special cases for our generalized results by using the ZipfMandelbrot law.
As applications, we present the majorization inequalities for various distances obtaining by some special convex
functions in the Csiszár fdivergence for ZM law like the
Rényi αorder entropy
for ZM law, variational distance for ZM law, the Hellinger distance for ZM law, χ^{2}distance for ZM law
and triangular discrimination for ZM law. At the end, we give important applications of the Zipf's
law in linguistics and obtain the bounds for the KullbackLeibler divergence of the distributions
associated to the English and the Russian languages.
Tbilisi Mathematical Journal, Vol. 11(3) (2018), pp. 127
