Generalized bit moments and cumulants based on discrete derivative

Abstract

We give a simple recipe based on the use of discrete derivative, to obtain generalized bit-moments obeying nonadditive statistics of Tsallis. The generalized bit-cumulants may be of two kinds, first which preserve the standard relations between moments and cumulants of a distribution, and are nonadditive with respect to independent subsystems. The second kind do not preserve usual moment-cumulant relations. These are additive in nature and Renyi entropy is naturally incorporated as the cumulant of order one.

Geometry of escort distributions

“…[7][8][9][10], in which statistical properties of chaotic dynamical systems are investigated. The ordinary bit-variance is recovered in the limit q → 1.…”