# Reply to "Comment on `R\'enyi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data' "

## TL;DR

This paper critiques Jizba and Korbel's comments on Re9nyi entropy, highlighting issues with their normalization, subset independence, and composition rule, and demonstrating that Re9nyi entropy introduces artificial biases.

## Contribution

The paper clarifies the limitations of Jizba and Korbel's approach, showing Re9nyi entropy's violations and biases, and emphasizes the importance of proper normalization and subset independence.

## Key findings

- Re9nyi entropy violates subset independence axiom
- Jizba and Korbel's composition rule creates artificial biases
- Proper normalization is crucial for entropy maximization

## Abstract

We reply to the Comment by Jizba and Korbel [arXiv:1905.00729v1] 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 must ingredient in the entropy maximization procedure. Secondly, 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 R\'enyi entropy violates the subset independence axiom and compare it with the Shannon entropy. Thirdly, the new composition rule offered by Jizba and Korbel are shown to yield probability distributions even without a need for the entropy maximization procedure at the expense of creating artificial bias in the data.