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.

previous

The Geometric Distribution

next

The Logarithmic Distribution