geometric distribution

Noun

 * 1) 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.
 * 2) * 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.
 * 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, 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, 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

 * Chinese:
 * Mandarin: 幾何分佈
 * Finnish: geometrinen jakauma
 * Kazakh: геометриялық таралым