# The Hypergeometric Distribution¶

gsl_ran_hypergeometric(p, n1, n2, t)

This function returns a random integer from the hypergeometric distribution. The probability distribution for hypergeometric random variates is,

$p(k) = C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t)$

where $$C(a,b) = a!/(b!(a-b)!)$$ and $$t \leq n_1 + n_2$$. The domain of $$k$$ is $$\max(0,t-n_2), ..., \min(t,n_1)$$.

If a population contains $$n_1$$ elements of “type 1” and $$n_2$$ elements of “type 2” then the hypergeometric distribution gives the probability of obtaining $$k$$ elements of “type 1” in $$t$$ samples from the population without replacement.

gsl_ran_hypergeometric_pdf(k, n1, n2, t)

This function computes the probability $$p(k)$$ of obtaining $$k$$ from a hypergeometric distribution with parameters n1, n2, t, using the formula given above.

gsl_cdf_hypergeometric_P(k, n1, n2, t)
gsl_cdf_hypergeometric_Q(k, n1, n2, t)

These functions compute the cumulative distribution functions $$P(k), Q(k)$$ for the hypergeometric distribution with parameters n1, n2 and t.