Latif Naveed, Pečarić Ðilda, Pečarić Josip
Department of Social Studies, Jubail Industrial College, Jubail, 31961 Kingdom of Saudi Arabia.
Catholic University of Croatia, Ilica 242, Zagreb, 10000 Croatia.
J Inequal Appl. 2017;2017(1):197. doi: 10.1186/s13660-017-1472-2. Epub 2017 Aug 24.
In this paper we show how the Shannon entropy is connected to the theory of majorization. They are both linked to the measure of disorder in a system. However, the theory of majorization usually gives stronger criteria than the entropic inequalities. We give some generalized results for majorization inequality using Csiszár -divergence. This divergence, applied to some special convex functions, reduces the results for majorization inequality in the form of Shannon entropy and the Kullback-Leibler divergence. We give several applications by using the Zipf-Mandelbrot law.
在本文中，我们展示了香农熵与优化理论是如何联系的。它们都与系统中的无序度量相关。然而，优化理论通常给出比熵不等式更强的准则。我们使用Csiszár散度给出了一些关于优化不等式的广义结果。这种散度应用于某些特殊的凸函数时，会以香农熵和库尔贝克 - 莱布勒散度的形式简化优化不等式的结果。我们通过使用齐普夫 - 曼德勃罗定律给出了几个应用。
