  Nonextensive statistics, characterized by a nonextensive parameter $q$, is a
promising and practically useful generalization of the Boltzmann statistics to
describe power-law behaviors from physical and social observations. We here
explore the unevenness of the first digit distribution of nonextensive
statistics analytically and numerically. We find that the first-digit
distribution follows Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the temperature. The fluctuation
decreases when $q$ increases, and the result converges to Benford's law exactly
as $q$ approaches 2. The relevant regularities between nonextensive statistics
and Benford's law are also presented and discussed.
