geometric distribution

== English == === Noun === geometric distribution (plural geometric distributions) Either of two slightly different discrete probability distributions, each based on repetitions of a trial with "success" probability p: (1) the number X of trials required to obtain one success, or (2) the number Y = X − 1 of failed trials before the first success. 2009, Matthew J. Hassett, Donald Stewart, Probability for Risk Management, 2nd Edition, ACTEX Publications, page 139, Recall that we have already calculated the mean and variance for the geometric distribution case (r = 1) in Example 5.17. ==== Usage notes ==== The two versions of the distribution differ in their range. Version (1) counts all trials, including the successful one, and has values ≥ 1. Version (2) counts only failures, and has values ≥ 0. The first is sometimes called the shifted geometric distribution, but it is considered better style to explicitly mention the difference in range. It is up to the writer to decide which is the geometric distribution. The distribution is a special case of the negative binomial distribution, which counts trials needed to reach n successes. It too is used in different versions. Sometimes, a writer may define the count as being made until the first "failure". This is logically equivalent, however, and the difference lies only in the interpretation of "success". ==== Translations ====