Brito López, RicardoRodriguez Navarro, Alonso2025-01-202025-01-202020-10Brito, R. and Rodriguez Alonso, A. The inconsistency of h-index: A mathematical analysis Journal of Informetrics, 15, 101106 (2021)1751-157710.1016/j.joi.2020.101106https://hdl.handle.net/20.500.14352/115138Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function, the equation that defines the h index can be formulated; this equation shows that h has a complex dependence on the number of papers (N). We also investigate the correlation between h and the number of papers exceeding various citation thresholds, from 5 to 500 citations. The best correlation is for the 100 threshold but numerous data points deviate from the general trend. The size-independent indicator h/N shows no correlation with the probability of publishing a paper exceeding any of the citation thresholds. In contrast with the h index, the total number of citations shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations. Thus, in synthetic series, the number of citations and the mean number of citations are much better indicators of research performance than h and h/N. We discuss that in real citation distributions there are other difficulties.engjournal article1875-5879https://doi.org/10.1016/j.joi.2020.101106https://www.sciencedirect.com/science/article/pii/S1751157720306234https://arxiv.org/abs/2002.06974open access001.8004h indexResearch assessmentCitationLognormal distributionBiblioteconomía y Documentación53 Ciencias Económicas