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.
This function computes the probability p(k) of obtaining k from a geometric distribution with probability parameter p, using the formula given above.
These functions compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter p.