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. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £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 |