Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity

Tytuł:: Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity
Autorzy:: Khuram Ali Khan
Tasadduq Niaz
Ðilda Pec̆arić
Josip Pec̆arić
Temat:: m-convex function
Jensen’s inequality
f- and Rényi divergence
Montgomery identity
Entropy
Mathematics
QA1-939
Źródło:: Journal of Inequalities and Applications, Vol 2018, Iss 1, Pp 1-22 (2018)
Wydawca:: SpringerOpen, 2018.
Rok publikacji:: 2018
Kolekcja:: LCC:Mathematics
Typ dokumentu:: article
Opis pliku:: electronic resource
Język:: English
ISSN:: 1029-242X
Relacje:: http://link.springer.com/article/10.1186/s13660-018-1902-9; https://doaj.org/toc/1029-242X
DOI:: 10.1186/s13660-018-1902-9
Dostęp URL:: https://doaj.org/article/f13a1074612d418eacbac522cb5012d0 Link otwiera się w nowym oknie
Numer akcesji:: edsdoj.f13a1074612d418eacbac522cb5012d0
: Czasopismo naukowe

Pełny tekst

Abstract Jensen’s inequality is important for obtaining inequalities for divergence between probability distribution. By applying a refinement of Jensen’s inequality (Horváth et al. in Math. Inequal. Appl. 14:777–791, 2011) and introducing a new functional based on an f-divergence functional, we obtain some estimates for the new functionals, the f-divergence, and Rényi divergence. Some inequalities for Rényi and Shannon estimates are constructed. The Zipf–Mandelbrot law is used to illustrate the result. In addition, we generalize the refinement of Jensen’s inequality and new inequalities of Rényi Shannon entropies for an m-convex function using the Montgomery identity. It is also given that the maximization of Shannon entropy is a transition from the Zipf–Mandelbrot law to a hybrid Zipf–Mandelbrot law.

Zaloguj się, aby uzyskać dostęp do pełnego tekstu.

Informacja