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.
翻译：科学家生产力和影响方面最常用的指标是出版物总数(N ⁇ pub}$)、引文总数(N ⁇ cit}$)和赫希指数(h)。自2005年赫希的原始论文以来,人们主要辩论的是,h指数是否可以被视为独立于$ ⁇ pub}美元和$ ⁇ cit}美元以外的指标。利用Paretian格式来分发一位研究人员撰写的论文的引文,这里我们讨论的是h、$ ⁇ pub}美元和$N ⁇ cit}之间的关系。分析包括吉尼指数,作为引用分布的不平等度衡量尺度,以及最近提出的不平等内核( ⁇ )问题。我们发现,作为引文总数的一个函数,即根据从谷歌学者收集的大量数据计算出的总数值,对h值有一个新的上限。我们的分析还表明,根据作者在0.8左右的社会-经济不平等程度的峰值计算出的个人化吉尼指数,通常比经济不平等程度高得多。
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