  The distribution function of the relative velocity in a two-body reaction of
nonrelativistic uncorrelated particles is derived for general cases of given
distribution functions of single particle velocities. The distribution function
is then used in calculations of thermonuclear reaction rates. As an example, we
take the Tsallis non-Maxwellian distribution, and show that the distribution
function of the relative velocity is different from the Tsallis distribution.
We identify an inconsistency in previous studies of nuclear reaction rates
within Tsallis statistics, and derive revised nuclear reaction rates. Utilizing
the revised rates, accurate results of big bang nucleosynthesis are obtained
for the Tsallis statistics. For this application it is more difficult to reduce
the primordial 7Li abundance while keeping other nuclear abundances within the
observational constraints. A small deviation from a Maxwell-Boltzmann
distribution can increase the D abundance and slightly reduce 7Li abundance.
Although it is impossible to realize a 7Li abundance at the level observed in
metal-poor stars, a significant decrease is possible while maintaining a
consistency with the observed D abundance.
