通过Leimkuhler曲线混合模型建模引文集中度
Modeling citation concentration through a mixture of Leimkuhler curves
AI总结：
本文针对标准Leimkuhler函数拟合信息计量数据精度不足的问题，提出将概率密度函数与异质性因子结合的新方法，引入PG和PIG混合分布并给出闭式表达式，实证表明混合模型优于基于Power和Pareto分布的基本模型。
摘要：
当将文章累计引用百分比（按引用次数从高到低排序）与文章累计百分比的图形表示绘制出来时，我们得到一条Leimkuhler曲线。在本研究中，我们注意到标准Leimkuhler函数可能不足以对各种实证信息计量学数据提供精确拟合。因此，我们引入一种新的Leimkuhler曲线方法，通过将已知概率密度函数拟合到初始Leimkuhler曲线，并考虑异质性因子的存在。作为对现有文献的重要贡献，我们将一对混合分布（称为PG和PIG）引入文献计量学。此外，我们给出了Leimkuhler曲线的闭式表达式。{针对基本模型（基于Power和Pareto分布）以及由这些模型导出的混合模型，实证检验了一些引文集中度指标。}对两个信息计量数据来源进行了应用，以考察混合模型如何优于标准基本模型。不同模型使用非线性最小二乘估计进行拟合。
英文摘要：
When a graphical representation of the cumulative percentage of total citations to articles, ordered from most cited to least cited, is plotted against the cumulative percentage of articles, we obtain a Leimkuhler curve. In this study, we noticed that standard Leimkuhler functions may not be sufficient to provide accurate fits to various empirical informetrics data. Therefore, we introduce a new approach to Leimkuhler curves by fitting a known probability density function to the initial Leimkuhler curve, taking into account the presence of a heterogeneity factor. As a significant contribution to the existing literature, we introduce a pair of mixture distributions (called PG and PIG) to bibliometrics. In addition, we present closed-form expressions for Leimkuhler curves. {Some measures of citation concentration are examined empirically for the basic models (based on the Power {and Pareto distributions}) and the mixed models derived from {these}.} An application to two sources of informetric data was conducted to see how the mixing models outperform the standard basic models. The different models were fitted using non-linear least squares estimation.
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