On the Distribution of the H-index

The h-index has been considered in terms of both unrestricted integer partitions and fuzzy integrals, and the expected value of h for a given number of citations has been estimated. However, the distribution of h as a function of both the number of citations and the number of papers has not been considered explicitly. Using Durfee squares determined from restricted integer partitions, it is shown that for a small number of papers the expected value of h estimated from the unrestricted partitions of the number of citations is unreliable. Despite this, it is confirmed that the distribution of his asymptotically normal. This means that h-indices should be considered in the context of the number of publications unless that number is large.