Inequalities for Information Potentials and Entropies

Abstract

We consider a probability distribution p0(x),p1(x),… depending on a real parameter x. The associated information potential is S(x):=∑kpk2(x). The Rényi entropy and the Tsallis entropy of order 2 can be expressed as R(x)=−logS(x) and T(x)=1−S(x). We establish recurrence relations, inequalities and bounds for S(x), which lead immediately to similar relations, inequalities and bounds for the two entropies. We show that some sequences Rn(x)n≥0 and Tn(x)n≥0, associated with sequences of classical positive linear operators, are concave and increasing. Two conjectures are formulated involving the information potentials associated with the Durrmeyer density of probability, respectively the Bleimann–Butzer–Hahn probability distribution.

Detecting Encrypted and Unencrypted Network Data Using Entropy Analysis and Confidence Intervals

“…According to what is described in Section 4 , high computing power is required in order to deal with the case of data without a known format, therefore the main goal of future studies is to improve the accuracy of the algorithm for Case Three (described in Section 3.7 ). For this, collaborations have been started for another variants, to implement evaluation systems of some additional entropy estimation parameters, according to the studies from [ 18 , 19 ]. Beyond this, as previously stated, is in our attention to adapt the current version to a solution that is suitable for implementation on low-power computing machines.…”