# The Negative Binomial Distribution¶

gsl_ran_negative_binomial(p, 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.

gsl_ran_negative_binomial_pdf(k, p, 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.

gsl_cdf_negative_binomial_P(k, p, n)
gsl_cdf_negative_binomial_Q(k, p, n)

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