The influence of the broadness of a query of a topic on its h-index: Models and examples of the h-index of N-grams

The article studies the influence of the query formulation of a topic on its h-Index. In order to generate pure random sets of documents, we used N-grams (N variable) to measure this influence: strings of zeros, truncated at the end. The used databases are WoS and Scopus. The formula h =T-1/alpha, proved in Egghe and Rousseau (2006) where T is the number of retrieved documents and a is Lotka's exponent, is confirmed being a concavely increasing function of T. We also give a formula for the relation between h and N the length of the N-gram: h = D10(-N/alpha). where D is a constant, a convexly decreasing function, which is found in our experiments. Nonlinear regression on h=T-1/alpha gives an estimation of alpha, which can then be used to estimate the h-index of the entire database (Web of Science [WoS] and Scopus): h=S-1/alpha, where S is the total number of documents in the database.