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

This function returns a random integer from the geometric distribution, the number of independent trials with probability p until the first success. The probability distribution for geometric variates is,

          p(k) =  p (1-p)^(k-1)

for k >= 1. Note that the distribution begins with k=1 with this definition. There is another convention in which the exponent k-1 is replaced by k.

— Function: double gsl_ran_geometric_pdf (unsigned int k, double p)

This function computes the probability p(k) of obtaining k from a geometric distribution with probability parameter p, using the formula given above.

— Function: double gsl_cdf_geometric_P (unsigned int k, double p)
— Function: double gsl_cdf_geometric_Q (unsigned int k, double p)

These functions compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter p.