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