In this Letter, we study the observed distributions of rotational velocity in a sample of more than 16,000 nearby F and G dwarf stars, magnitude complete, and presenting high-precision V sin i measurements. We show that the velocity distributions cannot be fitted by a Maxwellian. In addition, an analysis based on both Tsallis and Kaniadakis power-law statistics is by far the most appropriate statistics and gives a very good fit. It is also shown that single and binary stars have similar rotational distributions. This is the first time, to our knowledge, that these two new statistics have been tested for the rotation of such a large sample of stars, pointing solidly to a solution of the puzzling problem of the function governing the distribution of stellar rotational velocity.