Reply to "Comment on 'Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data'".

Abstract

We reply to the preceding Comment by Jizba and Korbel [Jizba and Korbel, Phys. Rev. E 100, 026101 (2019)10.1103/PhysRevE.100.026101] by first pointing out that the Schur concavity proposed by them falls short of identifying the correct intervals of normalization for the optimum probability distribution even though normalization is a necessary ingredient in the entropy maximization procedure. Second, their treatment of the subset independence axiom requires a modification of the Lagrange multipliers one begins with, thereby rendering the optimization less trustworthy. We also explicitly demonstrate that the Rényi entropy violates the subset independence axiom and compare it with the Shannon entropy. Third, the composition rule offered by Jizba and Korbel is shown to yield probability distributions even without a need for the entropy maximization procedure at the expense of creating artificial bias in the data.