The Hypergeometric Distribution¶
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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.
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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.
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gsl_cdf_hypergeometric_P(k, n1, n2, t)¶
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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,n2andt.