A statistical distribution that serves as a model for situations concerned with the number of successes per unit of observation, e.g. the number of phytoplankton caught per trawl. More strictly speaking, this is a limiting form of the binomial distribution when the probability of success for an individual trial approaches zero, the number of trials becomes infinite, and the product of these two quantities remains constant.

A statistical tool that assumes 3 conditions: for any one observation only two results are possible; the chances of these two results do not vary from one observation to the next; and successive observations are independent

discrete random variable X is said to follow a Poisson distribution with parameter m, written X ~ Po(m), if in a memoryless or completely random process, X represents a count of the number of random events that occur in a certain time interval or spatial area. For example, the number of cars passing a fixed point in a 5 minute interval; the number of calls received by a switchboard during a given period of time.

a theoretical distribution that is a good approximation to the binomial distribution when the probability is small and the number of trials is large

a probability distribution of a Poisson random variable

The distribution of the total number of successes in a large number of Bernoulli trials when the probability of success in each trial is very small.

Poisson distributions model (some) discrete random variables (i.e. variables that may take on only a countable number of distinct values, such as 0, 1, 2, 3, 4,....). Typically, a Poisson random variable is a count of the number of events that occur in a certain time interval or spatial area (statistics). [6

Mathematical function relating the number of particles in a given volume element to the average concentration of randomly distributed particles in the entire volume.1

Poisson distributions model (some) discrete random variables. Typically, a Poisson random variable is a count of the number of events that occur in a certain time interval or spatial area. For example, the number of cars passing a fixed point in a five minute interval.

Used in the description of discrete cyclone occurrence in limited domains; Section 9.7.

A distribution often used to express probabilities concerning the number of events per unit. For example, the number of computer malfunctions per year, or the number of bubbles per square yard in a sheet of glass, might follow a Poisson distribution. The distribution is fully characterized by its mean, usually expressed in terms of a rate. Parameters: mean B0 Domain: X=0,1,2,... Mean: B Variance: B

Probability function that is used for charts for defects.

A probability distribution that characterizes discrete events occurring independently of one another in time. See attenuation.

A mathematical expression giving the probability of observing various numbers of a particular event in a sample when the mean probability of an event on any one trial is very small.

A probability density function that is often used as a mathematical model of the number of outcomes obtained in a suitable interval of time and space.

A probability distribution used to model the number of times a rare event occurs.

The distribution giving the probability of obtaining exactly successes in trials for Poisson processes such as radioactive decay and lotteries.

A probability function used to model the density of counts of a randomly occurring event obtained during a specified interval of time.

A one-parameter, discrete frequency distribution giving the probability that points (or events) will be (or occur) in an interval (or time) , provided that these points are individually independent and that the number occurring in a subinterval does not influence the number occurring in any other nonoverlapping subinterval. It has the form (, ) = )/!. The mean and variance are both Îº, and Îº is the average density (or rate) with which the events occur. When Îº is large, the Poisson distribution approaches the normal distribution. The binomial distribution approaches the Poisson when the number of events becomes large and the probability of success becomes small in such a way that np. The Poisson distribution arises in such problems as radioactive and photoelectric emissions, thermal noise, service demands, and telephone traffic.

In probability theory and statistics, the Poisson distribution is a discrete probability distribution. It expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate, and are independent of the time since the last event.