Meaning of geometric distribution | Babel Free

Definitions

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.

Equivalents

Examples

“If S₁ had been chosen to be a geometric distribution, no a priori choices would have⟳ been necessary. This distribution was effective in Suppes (1970), but it would provide⟳ a poor fit in this case. If the geometric distribution had been used here, the parameter S₁ would have⟳ appeared in every theoretical probability involving N, and whenever one or more adjectives were included, a corresponding number⟳ of S₂ = 1 - S₁ terms would have⟳ appeared in the probability.”

“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.”

“The exponential distribution has a number⟳ of other interesting characteristics and properties. It is very similar to the geometric distribution, and in fact is the continuous version of that discrete distribution. Recall⟳ that the geometric distribution was used to model⟳ the time until the first success, where there were a discrete number⟳ of trials.”

CEFR level