Abstract We propose a simple stochastic model for an author's production/citation process in order to investigate the recently proposed h-index for measuring an author's research output and its impact. The parametric model distinguishes between an author's publication process and the subsequent citation processes of the published papers. This allows us to investigate different scenarios such as varying the production/publication rates and citation rates as well as the researcher's career length. We are able to draw tentative results regarding the dependence of Hirsch's h-index on each of these fundamental parameters. We conjecture that the h-index is, according to this model, (approximately) linear in career length, log publication rate and log citation rate, at least for moderate citation rates.