Some properties of Zipf-Mandelbrot law and Hurwitz ζ-function (CROSBI ID 254557)
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Podaci o odgovornosti
Jakšetić, Julije ; Pečarić, Đilda ; Pečarić, Josip
engleski
Some properties of Zipf-Mandelbrot law and Hurwitz ζ-function
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.
Zipf-Mandelbrot law ; Hurwitz ζ -function ; log-convexity ; Chebyshev’s inequality ; Lyapunov’s inequality
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