h指数不一致性的数学分析
The inconsistency of h-index: a mathematical analysis
摘要：
引文分布是对数正态分布。我们使用30个对数正态分布的合成数字序列，模拟真实的一系列引文调查的一致性的h指数。使用对数正态累积分布函数，可以公式化定义h指数的方程;该方程表明h对论文数量（N）具有复杂的依赖性。我们还调查了h和超过各种引用阈值的论文数量之间的相关性，从5到500次引用。最好的相关性是100阈值，但许多数据点偏离了总趋势。与论文大小无关的指标h/N与发表论文超过任何引用阈值的概率无关。与h指数相反，总引用次数与超过10次和50次引用阈值的论文数量高度相关;平均引用次数与发表超过任何引用水平的论文的概率相关。因此，在综合系列中，引文数和平均引文数是比h和h/N更好的研究绩效指标。我们讨论，在真正的引文分布有其他困难。
英文摘要：
Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function, the equation that defines the h index can be formulated; this equation shows that h has a complex dependence on the number of papers (N). We also investigate the correlation between h and the number of papers exceeding various citation thresholds, from 5 to 500 citations. The best correlation is for the 100 threshold but numerous data points deviate from the general trend. The size-independent indicator h/N shows no correlation with the probability of publishing a paper exceeding any of the citation thresholds. In contrast with the h index, the total number of citations shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations. Thus, in synthetic series, the number of citations and the mean number of citations are much better indicators of research performance than h and h/N. We discuss that in real citation distributions there are other difficulties.
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