If we have two information production processes with the same h-index, random removal of items causes one system to have a higher h-index than the other system while random removal of sources causes the opposite effect. In a Lotkaian framework we prove formulae for the h-index in case of random removal of items and in case of random removal of sources. In conclusion, we warn for the use of the h-index in case of incomplete data sets.
Banks, MG 2006 An extension of the Hirsch-index: Indexing scientific topics and compounds. Scientometrics 69 1 161–168 .
Braun, T, Glänzel, W, Schubert, A 2005 A Hirsch-type index for journals. The Scientist 19 22 8–10.
Braun, T, Glänzel, W, Schubert, A 2006 A Hirsch-type index for journals. Scientometrics 69 1 169–173 .
Burrell, Q. L. (2011). Private communication.
Egghe, L 2005 Power laws in the information production process: Lotkaian informetrics Elsevier Oxford.
Egghe, L 2008 The influence of transformations on the h-index and the g-index. Journal of the American Society for Information Science and Technology 59 8 1304–1312 .
Egghe, L 2008 Examples of simple transformations of the h-index: Qualitative and quantitative conclusions and consequences for other indices. Journal of Informetrics 2 2 136–148 .
Egghe, L. (2010a). The Hirsch-index and related impact measures. In B. Cronin (ed.), Annual review of information science and technology (Vol. 44, pp. 65–114). Medford: Information Today, Inc.
Egghe, L 2010 Influence of adding or deleting items and sources on the h-index. Journal of the American Society for Information Science and Technology 61 2 370–373 .
Egghe, L. (2010c). A disadvantage of h-type indices for comparing the impact of two researchers Research Evaluation (to appear).
Egghe, L. (2010d). Mathematical derivation of the scale-dependence of the h-index and other h-type indices Scientometrics, 87(2), 287-292.
Egghe, L, Rousseau, R 2006 An informetric model for the Hirsch-index. Scientometrics 69 1 121–129 .
Henzinger, M, Suñol, J, Weber, I 2010 The stability of the h-index. Scientometrics 84 2 465–479 .
Hirsch, JE 2005 An index to quantify an individual's scientific research output. Proceedings of the National Academy of Sciences of the United States of America 102 46 16569–16572 .
AFJ van Raan 2006 Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgment for 147 chemistry groups. Scientometrics 67 3 491–502.