The Geometric Distribution


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.