Bounds for Csiszár divergence and hybrid Zipf‐Mandelbrot entropy

Abstract

The purpose of this paper is to give a series of inequalities of the Jensen type and their applications for Csiszár divergence. By using these results, we give many estimations for hybrid Zipf-Mandelbrot entropy. KEYWORDSconvex functions, Csiszár divergence, hybrid Zipf-Mandelbrot entropy, Jensen's inequality, Slater's inequality MSC CLASSIFICATION 26D15; 94A17; 94A15 Math Meth Appl Sci. 2019;42:7411-7424. wileyonlinelibrary.com/journal/mma

Jensen‐Grüss inequality and its applications for the Zipf‐Mandelbrot law

“…The law itself is a discrete probability distribution defined by its probability mass function where and This law has various applications in linguistics, information sciences, economy (where it is known as the discrete Pareto law), and in ecological studies. Some recent results can be found for example in Adil Khan et al 9 and Jakšetić 10 . The Zipf‐Mandelbrot entropy is given by and the cumulative distribution function ( CDF ) is defined by …”