— Function: unsigned int gsl_ran_binomial (const gsl_rng * r, double p, unsigned int n)

This function returns a random integer from the binomial distribution, the number of successes in n independent trials with probability p. The probability distribution for binomial variates is,

          p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k}

for 0 <= k <= n.

— Function: double gsl_ran_binomial_pdf (unsigned int k, double p, unsigned int n)

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

— Function: double gsl_cdf_binomial_P (unsigned int k, double p, unsigned int n)
— Function: double gsl_cdf_binomial_Q (unsigned int k, double p, unsigned int n)

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