# The Geometric Distribution¶

gsl_ran_geometric(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 $$k \geq 1$$. Note that the distribution begins with $$k=1$$ with this definition. There is another convention in which the exponent $$k-1$$ is replaced by $$k$$.

gsl_ran_geometric_pdf(k, p)

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

gsl_cdf_geometric_P(k, p)
gsl_cdf_geometric_Q(k, p)

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