Pregled bibliografske jedinice broj: 1271385
Improvements of the inequalities for the f -divergence functional with applications to the Zipf-Mandelbrot law
Improvements of the inequalities for the f -divergence functional with applications to the Zipf-Mandelbrot law // Inequalities and Zipf-Mandelbrot law. Selected topics in information theory, Monographs in inequalities 15 / Pečarić, Ðilda ; Pečarić, Josip (ur.).
Zagreb: Element, 2019. str. 167-203
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Naslov
Improvements of the inequalities for the f -divergence functional with applications to the Zipf-Mandelbrot law
Autori
Butt, Saad Ihsan ; Horvath, Laszlo ; Pečarić, Ðilda ; Pečarić, Josip
Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni
Knjiga
Inequalities and Zipf-Mandelbrot law. Selected topics in information theory, Monographs in inequalities 15
Urednik/ci
Pečarić, Ðilda ; Pečarić, Josip
Izdavač
Element
Grad
Zagreb
Godina
2019
Raspon stranica
167-203
ISBN
978-953197-670-1
Ključne riječi
Convex function, f -divergence, inequalities for f -divergence, Jensen’s inequality, Shannon entropy
Sažetak
The Jensen’s inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this chapter, we introduce a new functional, based on the f -divergence functional, and then we obtain some estimates for the new functional, the f -divergence and the R´enyi divergence by applying a cyclic refinement of the Jensen’s inequality. Some inequalities for R´enyi and Shannon entropies are obtained too. Zipf-Mandelbrot law is used to illustrate the results.
Izvorni jezik
Engleski
Znanstvena područja
Matematika, Interdisciplinarne prirodne znanosti, Informacijske i komunikacijske znanosti, Interdisciplinarne društvene znanosti
POVEZANOST RADA
Ustanove:
Hrvatsko katoličko sveučilište, Zagreb
