Normalized fractional Hirsch Index and Modified Pareto Law
Abstract
The Hirsch index (introduced in 2005) has been a very successful scientometric author-level measure for the publication impact inequalities among the authors. However, it does not have any upper bound and statistically it grows in proportion to the square root of the number of publications by the author. Social scientists, on the other hand, measure the economic performance of different countries (having different wealth amounts and populations etc.) using inequality indices like the Gini index (since 1912) etc., which are normalized quantities (independent of the country's total wealth or the population size). We show here that a normalized fractional Hirsch index, giving the fraction of total citations earned by fraction of those successful papers published by the author, can even indicate that typically about 14% of the top cited papers earn about 86% of citations for very successful scientists (like the 95 Nobel Laureates considered here). This is similar to Pareto's 80-20 law (since 1896) and agrees more precisely with those observed for self-organized sandpile models, where typically 86% of the avalanche masses are dissipated through 14% of the largest avalanches as the piles approach their respective self-organized critical points.
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BibTeX
@misc{ghosh2026normalized,
title = {{Normalized fractional Hirsch Index and Modified Pareto Law}},
author = {Asim Ghosh and Bikas K. Chakrabarti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26710},
eprint = {2609.26710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26710},
note = {CC0},
}
RIS
TY - UNPB
TI - Normalized fractional Hirsch Index and Modified Pareto Law
AU - Asim Ghosh
AU - Bikas K. Chakrabarti
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.26710
UR - https://arxiv.org/abs/2609.26710
AB - The Hirsch index (introduced in 2005) has been a very successful scientometric author-level measure for the publication impact inequalities among the authors. However, it does not have any upper bound and statistically it grows in proportion to the square root of the number of publications by the author. Social scientists, on the other hand, measure the economic performance of different countries (having different wealth amounts and populations etc.) using inequality indices like the Gini index (since 1912) etc., which are normalized quantities (independent of the country's total wealth or the population size). We show here that a normalized fractional Hirsch index, giving the fraction of total citations earned by fraction of those successful papers published by the author, can even indicate that typically about 14% of the top cited papers earn about 86% of citations for very successful scientists (like the 95 Nobel Laureates considered here). This is similar to Pareto's 80-20 law (since 1896) and agrees more precisely with those observed for self-organized sandpile models, where typically 86% of the avalanche masses are dissipated through 14% of the largest avalanches as the piles approach their respective self-organized critical points.
ER -