Majorization, Csiszár divergence and Zipf-Mandelbrot law - Naveed Latif; Ðilda Pečarić; Josip Pečarić (Journal of Inequalities and Applications, 2017)
Abstract 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 f-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.