{
  "id": "2307.12110",
  "version": "v1",
  "published": "2023-07-22T15:41:14.000Z",
  "updated": "2023-07-22T15:41:14.000Z",
  "title": "How to estimate the total number of citations of a researcher using his h index and his h core?",
  "authors": [
    "Romeo Mestrovic",
    "Branislav Dragovic"
  ],
  "comment": "59 pages, 14 tables, two figures. Every comment is welcome",
  "categories": [
    "math.CO",
    "cs.DM",
    "physics.soc-ph"
  ],
  "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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-22T15:41:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "total number",
      "researcher",
      "asymptotic formula",
      "small additional citations",
      "errors delta"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}