— Function: unsigned int gsl_ran_poisson (const gsl_rng * r, double mu)

This function returns a random integer from the Poisson distribution with mean mu. The probability distribution for Poisson variates is,

          p(k) = {\mu^k \over k!} \exp(-\mu)

for k >= 0.

— Function: double gsl_ran_poisson_pdf (unsigned int k, double mu)

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

— Function: double gsl_cdf_poisson_P (unsigned int k, double mu)
— Function: double gsl_cdf_poisson_Q (unsigned int k, double mu)

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