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- W4299993109 abstract "Let P=(p1, ..., pn)be a probability distribution on a setΩ={ω1, ..., ωn}with n elements, n ∈ N{1}. Then the termS2(P)=1−Íni=1p2i,frequently called the Gini–Simpson index, or, in information theory, quadratic entropy, is used in many different areas of research resp. applications and was, therefore, reinvented several times. In this note we give aconcise history of this index and closely related measures, as well as its generalisation to allvalues of the parameter of the class of entropies of orderα∈(0,∞){1}introduced by Havrda and Charvát(1967) and reinvented by Tsallis(1988) for the use of this index in statistical physics, for which the limiting case forα→1isShannon’s entropyS1(P)=−Íni=1pilnpi.We also give a brief note on weighted versions of the Gini–Simpson index.In addition to these central historic features our note also presents contributions on the axiomatics of entropies and on the early history of the application of the concept of entropyin thermodynamics. We also provide an entry on Rényi’s class of entropies, linked with Hill’s diversity numbers" @default.
- W4299993109 created "2022-10-03" @default.
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- W4299993109 date "2018-01-01" @default.
- W4299993109 modified "2023-09-30" @default.
- W4299993109 title "On the Gini–Simpson index and its generalisation—A historic note" @default.
- W4299993109 doi "https://doi.org/10.37920/sasj.2018.52.2.2" @default.
- W4299993109 hasPublicationYear "2018" @default.
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