A general non-central hypergeometric distribution

We construct a general non-central hypergeometric distribution, which models biased sampling without replacement. Our distribution is constructed from the combined order statistics of two samples: one of independent and identically distributed random variables with absolutely continuous distribution F and the other of independent and identically distributed random variables with absolutely continuous distribution G. The distribution depends on F and G only through F○G^{( ? 1)} (F composed with the quantile function of G), and the standard hypergeometric distribution and Wallenius’ non-central hypergeometric distribution arise as special cases. We show in efficient economic markets the quantity traded has a general non-central hypergeometric distribution.