New estimates for generalized Shannon and Zipf-Mandelbrot entropies via convexity results

Abstract

Shannon and Zipf-Mandelbrot entropies have several applications in various fields such as ecology, statistics, physics and information theory etc. The aim of this article is to utilize some results of Jensen’s inequality for convex functions and to present several new estimates for generalized Zipf-Mandelbrot and Shannon entropies. In particular, we deduce estimates for Shannon and Zipf-Mandelbrot entropies which are different from the estimates obtained earlier using the same results of Jensen’s inequality. This way of obtaining the results for these entropies may open a new door to obtain several other estimates by using results for convex functions.

Keywords

• Jensen inequality
• Convex function
• Shannon entropy
• Zipf-Mandelbrot entropy