geometric distribution

plural geometric distributions

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.

   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.

   2 more 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.

   1973, Elizabeth M. Gammon, “A Syntactical Analysis of Some First-Grade Readers”, in K. J. J. Hintikka, P. Suppes, J.M.E. Moravcsik, editors, Approaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics, Springer, page 122

   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.

   2010, Peter A. Rogerson, Statistical Methods for Geography: A Student's Guide, 3rd edition, SAGE Publications, page 92