Poisson distribution

A discrete probability distribution for counts of events in a fixed interval, characterized by an average rate and independent event occurrences.

Poisson probability mass function: The formula assigning probability to each nonnegative integer count under a Poisson distribution. It calculates each count probability from the rate parameter.
Probability mass function: A function assigning probabilities to the possible values of a discrete random variable. The Poisson distribution is specified by this kind of function.
Poisson regression: A generalized linear model for count outcomes whose conditional mean is linked to explanatory variables. It extends Poisson counts to rates that vary with measured predictors.
Binomial distribution: A discrete distribution for the number of successes in a fixed number of independent trials with equal success probability. It models bounded trial counts, while Poisson counts are unbounded and often approximate rare successes.
Poisson process: A stochastic process whose independent increments count events arriving at a constant rate. Its interval counts have Poisson distributions.
Expected value: The probability-weighted average value of a random variable. For a Poisson distribution, the expected count equals its rate parameter.
Poisson point process: A random arrangement of points in space or time with independent counts in disjoint regions. It applies Poisson counting to event locations as well as totals.
Geometric distribution: A discrete distribution for the number of independent trials needed to obtain the first success. It counts trials until an event rather than events within a fixed interval.
Exponential distribution: A continuous probability distribution commonly used to model waiting times between events in a Poisson process. It describes the gaps between events whose counts follow this distribution.
Variance: A measure of how far a random variable's values typically vary from their mean. Its equality with the mean is a defining feature of the Poisson model.

Linked from 27 pages