科学计量指标的 Gintropic 标度
Gintropic Scaling of Scientometric Indexes
AI总结：
本文基于引文分布的 Paretian 形式、Gini 指数与 gintropy 核，推导 h 指数、论文数和被引次数的标度关系，并用 Google Scholar 大规模数据验证 h 的新上界。
摘要：
衡量科学生产力和影响力最常用的指标是论文总数（$N_{pub}$）、总被引次数（$N_{cit}$）以及 Hirsch（h）指数。自 Hirsch 于 2005 年发表开创性论文以来，h 指数能否被视为独立于 $N_{pub}$ 和 $N_{cit}$ 的指标一直存在广泛争议。本文利用研究人员所著论文引文分布的 Paretian 形式，讨论了 h、$N_{pub}$ 与 $N_{cit}$ 之间的标度关系。该分析将 Gini 指数作为引文分布的不平等度量，并纳入了最近提出的、类似于熵核的不平等核 gintropy。我们发现了一个以总被引次数为函数的 h 值新上界，并在从 Google Scholar 收集的大规模数据上得到证实。分析还表明，针对一位作者的论文所获引文计算的个体化 Gini 指数在约 0.8 处达到峰值，这一数值远高于通常社会经济不平等所特有的水平。
英文摘要：
The most frequently used indicators for the productivity and impact of scientists are the total number of publication ($N_{pub}$), total number of citations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of $N_{pub}$ and $N_{cit}$. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, $N_{pub}$ and $N_{cit}$. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confimed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one characteristic for the usual socio-economic inequalities.
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