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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)

## 19.33 The Negative Binomial Distribution

Function: unsigned int gsl_ran_negative_binomial (const gsl_rng * r, double p, double n)
This function returns a random integer from the negative binomial distribution, the number of failures occurring before n successes in independent trials with probability p of success. The probability distribution for negative binomial variates is,
p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k


Note that n is not required to be an integer.

Function: double gsl_ran_negative_binomial_pdf (unsigned int k, double p, double n)
This function computes the probability p(k) of obtaining k from a negative binomial distribution with parameters p and n, using the formula given above.

Function: double gsl_cdf_negative_binomial_P (unsigned int k, double p, double n)
Function: double gsl_cdf_negative_binomial_Q (unsigned int k, double p, double n)
These functions compute the cumulative distribution functions P(k), Q(k) for the negative binomial distribution with parameters p and n.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition