Geometric Distributions

Geometric distributions are unlike other types of distributions in that they are discrete, memoryless, and random. The dictionary definition of a geometric distribution is a distribution of the number of trials required to reach a first success. Because this distribution is memoryless  past trials do not influence future outcomes. In regards to determining rates of success then, past failures would not influence the probability of future successes. Thus, if you considered a success to be a coin landing heads up, all coin tosses that landed tails side up would essentially be "forgotten". The continuous analogue to the geometric distribution is the exponential distribution. The geometric distribution can be used to estimate the parameter, p, by equating expected values with the sample mean. This estimated parameter, p, is referred to as the success parameter. When this success parameter is positive, it is impossible to run trials infinitely without ever achieving some successes.