The Poisson Distribution

gsl_ran_poisson(mu)

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

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

for \(k \geq 0\).

gsl_ran_poisson_pdf(k, mu)

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

gsl_cdf_poisson_P(k, mu)

gsl_cdf_poisson_Q(k, mu)

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

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The Type-2 Gumbel Distribution

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The Bernoulli Distribution