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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 19.36 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.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition