Naslov
Majorizatiuon and Zipf-Mandelbrot law

Autori
Latif, Naveed ; Pečarić, Đilda ; Pečarić, Josip

Izvornik
Tbilisi mathematical journa (1875-158X) 11 (2018), 3; 1-27

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
χ2-distance and triangular discrimination , Csiszár f-divergence , Hellinger discrimination , Majorization inequailty , Rényi α-order entropy , variational distance , Zipf-Mandelbrot law , Zipf's law in linguistic

Sažetak
In this paper we show how the Zipf-Mandelbrot law is connected to the theory of majorization. Firstly we consider the Csiszár f-divergence for the Zipf-Mandelbrot law and then develop important majorization inequalities for these divergences. We also discuss some special cases for our generalized results by using the Zipf-Mandelbrot law. As applications, we present the majorization inequalities for various distances obtaining by some special convex functions in the Csiszár f-divergence for Z-M law like the Rényi α-order entropy for Z-M law, variational distance for Z-M law, the Hellinger distance for Z-M law, χ2-distance for Z-M law and triangular discrimination for Z-M law. At the end, we give important applications of the Zipf's law in linguistics and obtain the bounds for the Kullback-Leibler divergence of the distributions associated to the English and the Russian languages.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Informacijske i komunikacijske znanosti

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