What is it: The Geometric Distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the Geometric Distribution is negative binomial distribution where the number of successes (r) is equal to 1. A geometric random variable is the number of trials required to obtain the first failure, for example, the number of tosses of a coin untill the first 'tail' is obtained, or a process where components from a production line are tested, in turn, until the first defective item is found.
Why use it: The Geometric Distribution is discrete, existing only on the nonnegative integers. It is useful for modeling the runs of consecutive successes (or failures) in repeated independent trials of a system. The Geometric Distribution models the number of successes before one failure in an independent succession of tests where each test results in success or failure.
