About "On certain incomplete statistics" by Lima et al

TL;DR

The paper critiques Lima et al's claim about the entropy formula in incomplete statistics, arguing that their conclusion stems from an incorrect temperature definition, thus clarifying the proper form of the entropy.

Contribution

It clarifies the correct entropy formulation in incomplete statistics by identifying errors in previous temperature assumptions.

Findings

Lima et al's entropy formula is based on an erroneous temperature definition.

Correct formulation of entropy in incomplete statistics is different from previous claims.

The paper emphasizes proper temperature definition is crucial for accurate entropy calculation.

Abstract

Lima et al recently claim that ({\em Chaos, Solitons $&$ Fractals,} 2004;19:1005)the entropy for the incomplete statistics based on the normalization$\sum_ip_i^q=1$ should be $S=-\sum_ip_i^{2q-1}\ln_qp_i$ instead of$S=-\sum_ip_i^{q}\ln_qp_i$ initially proposed by Wang. We indicate here that thisconclusion is a result of erroneous use of temperature definition for the incompletestatistics.