Geometric Distribution

(discrete probability dist. for equations)

 

Usage:

GeometricDist (k, p)

Definition:

p (1-p)^ k

Required:

0 < p ⋜ 1     k is an integer

Support:

0 ⋜ k

Moments:

μ = (1-p) / p

σ^2 = (1-p) / p^2

γ1 = (2-p) / sqrt (1-p)

β2 = 3 + [p^2 + 6 (1-p)] / (1-p)

This distribution describes the number of Bernoulli trials (independent trials, with outcomes labeled "success" or "failure", and constant probability p of success) before the first success occurs (i.e., includes only the failure trials).  An example would be the number of coin flips resulting in tails before the first head is seen.

Situations where Bernoulli trials are repeated until the nth success are called "negative binomial experiments", and the geometric distribution is a special case of the negative binomial distribution with n = 1.

Note that the geometric distribution is instead defined by some authors to have the pdf: p (1-p)^(k-1)