A general non-central hypergeometric distribution

Simon Loertscher, Ellen V. Muir and Peter G. Taylor

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 9, 4579-4598

Abstract: 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.

Date: 2017
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DOI: 10.1080/03610926.2015.1088033

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