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Fisher’s Noncentral Hypergeometric Distribution¶
A random variable has Fisher’s Noncentral Hypergeometric distribution with parameters
\(M \in {\mathbb N}\), \(n \in [0, M]\), \(N \in [0, M]\), \(\omega > 0\),
if its probability mass function is given by
for \(x \in [x_l, x_u]\), where \(x_l = \max(0, N - (M - n))\), \(x_u = \min(N, n)\),
and the binomial coefficients are
Other functions of this distribution are
References¶
Agner Fog, “Biased Urn Theory”, https://cran.r-project.org/web/packages/BiasedUrn/vignettes/UrnTheory.pdf
“Fisher’s noncentral hypergeometric distribution”, Wikipedia, https://en.wikipedia.org/wiki/Fisher’s_noncentral_hypergeometric_distribution
Implementation: scipy.stats.nchypergeom_fisher