Moments of the generalized distribution for stellar rotation rates

In order to obtain the moments of different theoretical distributions and compare them with those obtained from distributions of true rotational rates, we derive the moments of the generalized distribution function of the projected rotational velocities V sin i and the true equatorial rotational velocities V from the Tsallis q-statistical formalism, then we compare such moments with others obtained via the conventional method. We show that the moments are constrained to intervals of validity for q larger than those for standard moments, thus it is possible to obtain distribution function broader than the standard cases. The variances show that the distributions become narrower around the mean as q decreases. We now should highlight that one can derive averages of sin i smaller than unity even if qV ≠ qV sin i.