归一化分数 Hirsch 指数与修正帕累托定律
Normalized fractional Hirsch Index and Modified Pareto Law
- Raghunathpur College（拉格纳特普尔学院）
- Indian Statistical Institute（印度统计研究所）
- Saha Institute of Nuclear Physics（萨哈核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出归一化分数 Hirsch 指数，发现诺贝尔奖得主约14%高被引论文获得86%引用，类似帕累托定律，并关联自组织临界现象。
AI中文摘要：
Hirsch 指数（于 2005 年提出）一直是衡量作者之间发表影响不平等的非常成功的科学计量学作者级指标。然而，它没有任何上限，并且在统计上它随作者发表论文数量的平方根成比例增长。另一方面，社会科学家使用诸如基尼指数（自 1912 年起）等不平等指数来衡量不同国家（具有不同财富总量和人口等）的经济表现，这些指数是归一化量（与国家的总财富或人口规模无关）。我们在此表明，一个归一化的分数 Hirsch 指数，给出作者发表的那些成功论文中某一比例所获得的总引用次数的比例，甚至可以表明，对于非常成功的科学家（如本文考虑的 95 位诺贝尔奖获得者），通常约 14% 的高被引论文获得了约 86% 的引用。这类似于帕累托的 80-20 定律（自 1896 年起），并且更精确地与自组织沙堆模型中观察到的结果一致，在该模型中，当沙堆接近其各自的自组织临界点时，通常约 86% 的雪崩质量通过 14% 的最大雪崩消散。
英文摘要：
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.
