How to estimate the total number of citations of a researcher using his h index and his h core?

TL;DR

This paper introduces a novel method to estimate a researcher's total citations using their h index, h core, and a few tail citations, based on asymptotic formulas related to the Durfee square, with promising accuracy demonstrated on real data.

Contribution

It proposes new estimation formulas for total citations from h index and tail citations, leveraging asymptotic normality of the h index, extending prior work.

Findings

Estimates show low relative error for well-known researchers.

Asymptotic formulas effectively predict total citations.

Refined estimates improve accuracy with minimal tail data.

Abstract

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).