Superquadratic functions in information theory
Josipa Barić, Đilda Pečarić, Josip E. Pečarić · Journal of Mathematical Inequalities · 2020
Using Jensen's inequality and the converse Jensen's inequality for superquadratic functions we obtain new estimates for Shannon's entropy of the random variable X and derive new lower and upper bounds for the Shannon entropy in the terms of the Zipf and Zipf-Mandelbrot's law.