Naslov
Combinatorial improvements of Zipf-Mandelbrot laws wia interpolations

Autori
Khan, Khuram Ali ; Nia, Tasadduq ; 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
129-164

ISBN
978-953197-670-1

Ključne riječi
Jensens inequality, Montgomery identity, Lidstone polynomial, Taylor polynomial, Hermite interpolating polynomial, Shannon entropies, Zipf-Mandelbrot Laws

Sažetak
Jensens inequality is important to obtain inequalities for divergence between probability distributions. By applying a refinement of Jensen inequality [17] and introducing a new functional based on f -divergence functional, we obtain some estimates for the new functionals, the f -divergence and R´enyi divergence. Some inequalities for R´enyi and Shannon estimates are constructed. Zipf-Mandelbrot law is used to illustrate the results and generalize the refinement of Jensens inequality and new inequalities of R´enyi and Shannon entropies for m-convex function using Montgomery identity, Lidstone polynomial, Taylor polynomial and Hermite interpolating polynomial.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Interdisciplinarne prirodne znanosti, Informacijske i komunikacijske znanosti, Interdisciplinarne društvene znanosti

POVEZANOST RADA