GNU Scientific Library – Reference Manual: The Negative Binomial Distribution

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### 20.34 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.