The geometric distribution is a discrete probability distribution with probability function given by:

subject to the following conditions:

The geometric distribution has the lack of memory property: the probability of an event occurring in the next time interval of an exponential distribution is independent of the amount of time that has already passed.

The geometric variate is a special case of the NegativeBinomial variate with number of trials parameter .

The continuous analog of the geometric variate is the Exponential variate.

Note that the Geometric command is inert and should be used in combination with the RandomVariable command.

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.