Some properties of Zipf-Mandelbrot law and Hurwitz ζ-function
| Autor: | Đilda Pečarić, Julije Jakšetić, Josip Pečarić |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
010101 applied mathematics
Zipf–Mandelbrot law Pure mathematics Zipf-Mandelbrot law Hurwitz ζ -function log-convexity Chebyshev’s inequality Lyapunov’s inequality Applied Mathematics General Mathematics 010102 general mathematics Function (mathematics) 0101 mathematics 01 natural sciences Mathematics |
| Popis: | In this paper we deal with analytical properties of the Zipf-Mandelbrot law. If total mass of this law is spread all over positive integers we come to Hurwitz ζ -function. As we show, it is very natural first to examine properties of Hurwitz ζ -function to derive properties of Zipf-Mandelbrot law. Using some well-known inequalities such as Chebyshev’s and Lyapunov’s inequality we are able to deduce a whole variety of theoretical characterizations that include, among others, log-convexity, log-subadditivity, exponential convexity. |
| Databáze: | OpenAIRE |
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