  The distribution of trade sizes and trading volumes are investigated based on
the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen
Stock Exchange in the whole year 2003. We observe that the size distribution of
trades for individual stocks exhibits jumps, which is caused by the number
preference of traders when placing orders. We analyze the applicability of the
"$q$-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises
criterion. The empirical PDFs of trading volumes at different timescales
$\Delta{t}$ ranging from 1 min to 240 min can be well modeled. The
applicability of the $q$-Gamma functions for multiple trades is restricted to
the transaction numbers $\Delta{n}\leqslant8$. We find that all the PDFs have
power-law tails for large volumes. Using careful estimation of the average tail
exponents $\alpha$ of the distribution of trade sizes and trading volumes, we
get $\alpha>2$, well outside the L{\'e}vy regime.
