


The Negative Binomial Distribution
==================================

.. function:: gsl_ran_negative_binomial(p, n)

 This function returns a random integer from the :index:`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,

 .. math::
   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:: gsl_ran_negative_binomial_pdf(k, p, n)

 This function computes the probability :math:`p(k)` of obtaining :math:`k` from
 a negative binomial distribution with parameters ``p`` and ``n``,
 using the formula given above.

.. function:: gsl_cdf_negative_binomial_P(k, p, n)

.. function:: gsl_cdf_negative_binomial_Q(k, p, n)

 These functions compute the cumulative distribution functions
 :math:`P(k), Q(k)` for the negative binomial distribution with parameters
 ``p`` and ``n``.
