The Hypergeometric Distribution - GNU Scientific Library -- Reference Manual
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### 20.36 The Hypergeometric Distribution

— Function: unsigned int gsl_ran_hypergeometric (const gsl_rng * r, unsigned int n1, unsigned int n2, unsigned int 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 <= 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.

— Function: double gsl_ran_hypergeometric_pdf (unsigned int k, unsigned int n1, unsigned int n2, unsigned int 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.

— Function: double gsl_cdf_hypergeometric_P (unsigned int k, unsigned int n1, unsigned int n2, unsigned int t)
— Function: double gsl_cdf_hypergeometric_Q (unsigned int k, unsigned int n1, unsigned int n2, unsigned int t)

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

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