如何利用研究者的h指数和h核心估计其总被引次数？
How to estimate the total number of citations of a researcher using his h index and his h core?
AI总结：
该研究反向探究h指数相关问题，借助Durfee square众数大小的渐近公式，提出五种结合h指数、h核心及尾部少量被引数据的总被引次数估计方法，实验显示部分学者的估计相对误差接近零。
AI中文摘要：
截至目前，已有众多研究者探讨了如下问题：给定总被引次数，h指数的估计范围是多少？本文则研究其反向问题，即仅利用研究者的h指数、h核心，或许再加上其被引分布尾部中数量相对较少的一部分被引数据，来估计该研究者的总被引次数。为此，我们使用了当n趋于无穷时Durfee square（德菲方形）众数大小的渐近公式，该公式由Canfield、Corteel和Savage于1998年证明，比Hirsch在2005年定义h指数早了七年，且该公式证实了Hirsch被引h指数的渐近正态性。利用这一渐近公式，我们在第4节提出了五种利用研究者h指数和h核心估计其总被引次数的方法，这些估计主要通过引入研究者h尾部的少量额外被引数据进行优化。第5节给出了相关的大量计算结果。值得注意的是，对于E. Garfield、H.D. White（表2）、G. Andrews、L. Leydesdorf和C.D. Savage（表5），总被引次数估计值B的相对误差δ(B)惊人地接近于零。
英文摘要：
So far, many researchers have investigated the following question: Given total number of citations, what is the estimated range of the h index? Here we consider the converse question. Namely, the aim of this paper is to estimate the total number of citations of a researcher using only his h index, his h core and perhaps a relatively small number of his citations from the tail. For these purposes, we use the asymptotic formula for the mode size of the Durfee square when n tends to infinity, which was proved by Canfield, Corteel and Savage (1998), seven years before Hirsch (2005) defined the h index. This formula confirms the asymptotic normality of the Hirsch citation h index. Using this asymptotic formula, in Section 4 we propose five? estimates of a total number of citations of a researcher using his h index and his h core. These estimates are refined mainly using small additional citations from the h tail of a researcher. Related numerous computational results are given in Section 5. Notice that the relative errors delta(B) of the estimate B of a total number of citations of a researcher are surprisingly close to zero for E. Garfield, H.D. White (Table 2), G. Andrews, L. Leydesdorf and C.D. Savage (Table 5).
