A toy model for the distribution of the impact factor (IF) of a journal is proposed. The model demonstrates the presence of a heavy tail for the IF distribution, which occurs due to some random non-scientific circumstances. Therefore, the use of IF as an indicator of the quality of scientific papers seems to be inadequate.

Different variants of thinning for discrete random variables are studied. The thinning procedure allows to introduce an analog of scale parameter for positive integer-valued random variables. Sufficient and necessary conditions for the existence of such a scale are given.