The inconsistency of h-index: A mathematical analysis

Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real citations to investigate the consistency h index. Using lognormal cumulative distribution function, equation defines index can be formulated; this shows has a complex dependence on number papers (N). also correlation between and exceeding various citation thresholds, from 5 500 citations. The best is for 100 threshold but numerous data points deviate general trend. size-independent indicator h/N no with probability publishing paper any thresholds. In contrast index, total high thresholds 10 50 citations; mean correlates exceeds level Thus, in series, much better indicators research performance than h/N. discuss there other difficulties.