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# Topic: Poisson distribution

###### In the News (Thu 6 Mar 14)

 Poisson Distributions The Poisson distribution describes a wide range of phenomena in the sciences. However, the important property of processes described by the Poisson distribution is that the SD is the square root of the total counts registered To illustrate, the table shows the results of counting our radioactive sample for different time intervals (with some artificial variability thrown in). Bernoulli distribution: This is used to describe discrete outcomes in trials such as coin-flipping, dice throwing, or the number and probabilities of DNA base pair changes. www.bio.cmu.edu /Courses/03438/PBC97Poisson/PoissonPage.html   (1934 words)

 Definition: Poisson distribution (January 19, 2007) For the Poisson distribution, the variance, λ;, is the same as the mean, so the standard deviation is √λ. Professor Mean explains that the Poisson distribution often arises when you are counting events in a certain area or time interval. Poisson data tends to have distibution that is skewed to the right, though it becomes closer to symmetric as the mean of the distribution increases. www.childrens-mercy.org /stats/definitions/poisson.htm   (1309 words)

 Poisson distribution The binomial distribution with parameters n and λ/n, i.e., the probability distribution of the number of successes in n trials, with probability λ/n of success on each trial, approaches the Poisson distribution with expected value λ as n approaches infinity. The higher moments of the Poisson distribution are Touchard polynomials in λ, whose coefficients have a combinatorial meaning. All of the cumulants of the Poisson distribution are equal to the expected value λ. publicliterature.org /en/wikipedia/p/po/poisson_distribution.html   (817 words)

 Tales of Statisticians | Siméon-Denis Poisson Poisson was born to modestly situated parents, and owed his career to the new scientific institutions created by the Revolution, which systematically sought and advanced students of promise. Poisson's Law of Large Numbers (1835), a generalization of Bernoulli and an advance on de Moivre, was the direct inspiration for Quetelet, and determined the direction of what is called the Continental school of statistics. This was the Poisson distribution, which predicts the pattern in which random events of very low probability occur in the course of a very large number of trials. www.umass.edu /wsp/statistics/tales/poisson.html   (790 words)

 Poisson distribution Summary The Poisson distribution is a mathematical rule that assigns probabilities to the number of occurrences of a certain event. Albert Einstein used Poisson noise to show that matter was composed of discrete atoms and to estimate Avogadro's number; he also used Poisson noise in treating flbody radiation to demonstrate that electromagnetic radiation was composed of discrete photons. For temporally distributed events, the Poisson distribution is the probability distribution of the number of events that would occur within a preset time, the Erlang distribution is the probability distribution of the amount of time until the nth event. www.bookrags.com /Poisson_distribution   (2272 words)

 Poisson biography Poisson was named deputy professor at the École Polytechnique in 1802, a position he held until 1806 when he was appointed to the professorship at the École Polytechnique which Fourier had vacated when he had been sent by Napoleon to Grenoble. The Poisson distribution describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. Poisson never wished to occupy himself with two things at the same time; when, in the course of his labours, a research project crossed his mind that did not form any immediate connection with what he was doing at the time, he contented himself with writing a few words in his little wallet. www-groups.dcs.st-and.ac.uk /~history/Biographies/Poisson.html   (2581 words)

 Poisson Distribution   (Site not responding. Last check: ) The poisson distribution is used to model rates, such as rabbits per acre, defects per unit, or arrivals per hour. For a random variable to be poisson distributed, the probability of an occurrence in an interval must be proportional to the length of the interval, and the number of occurrences per interval must be independent. The poisson cumulative distribution function is simply the sum of the poisson probability density function from 0 to x. www.engineeredsoftware.com /lmar/poisson.htm   (495 words)

 News | TimesDaily.com | TimesDaily | Florence, AL   (Site not responding. Last check: ) The Poisson distribution is sometimes called a Poissonian, analagous to the term Gaussian for a Gauss or normal distribution. The Poisson distribution can be derived as a limiting case to the binomial distribution as the number of trials goes to infinity and the expected number of successes remains fixed. For temporally distributed events, the Poisson distribution is the probability distribution of the number of events that would occur within a preset time, the Erlang distribution is the probability distribution of the amount of time until the nth event. www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Poisson_distribution   (1983 words)

 Poisson Process The Poisson random variable is characterized by a value λ=μ (the mean) which indicates the average number of events in the given time interval.. The distribution associated with the Poisson random variable is the Poisson distribution. MEDICINE - The Poisson Distribution can be used to count the number of victims of specific diseases, such as the number of cancer deaths per house, or the number of malaria deaths per year. www2.umassd.edu /CISW3/coursepages/pages/cis362/problems/poisson/explanation.html   (752 words)

 1.3.6.6.19. Poisson Distribution The Poisson distribution is used to model the number of events occurring within a given time interval. Note that because this is a discrete distribution that is only defined for integer values of x, the percent point function is not smooth in the way the percent point function typically is for a continuous distribution. Most general purpose statistical software programs, including Dataplot, support at least some of the probability functions for the Poisson distribution. www.itl.nist.gov /div898/handbook/eda/section3/eda366j.htm   (175 words)

 The Poisson Distribution The Poisson Distribution is a discrete distribution which takes on the values X = 0, 1, 2, 3,... It is often used as a model for the number of events (such as the number of telephone calls at a business or the number of accidents at an intersection) in a specific time period. The Poisson distribution is determined by one parameter, lambda. www.math.csusb.edu /faculty/stanton/m262/poisson_distribution/Poisson_old.html   (141 words)

 The Poisson Distribution online. For the statistical analysis of rare events and accidents The main differences between the poisson distribution and the binomial distribution is that in the binomial all eligible phenomena are studied, whereas in the poisson distribution only the cases with a particular outcome are studied. One assumption in this application of the poisson distribution is that the chance of having an accident is randomly distributed: every individual has an equal chance. Mathematically this is expressed in the fact that the variance and the mean for the poisson distribution are equal. home.clara.net /sisa/poishlp.htm   (761 words)

 Poisson distribution distribution is the distribution of the number of events in a fixed time interval, provided that the events occur at random, independently in time and at a constant rate. Both the mean and variance of a Poisson distribution are equal to µ. Other common uses of Poisson are in Physics to model radioactive particle emission and in insurance companies to model accident rates. www.statsdirect.com /help/distributions/pp.htm   (310 words)

 Poisson Distribution   (Site not responding. Last check: ) Other phenomena that often follow a poisson distribution are death of infants, the number of misprints in a book, the number of customers arriving, and the number of activations of a geiger counter. However, if we want to use the binomial distribution we have to know both the number of people who make it safely from A to B, and the number of people who have an accident while driving from A to B, whereas the number of accidents is sufficient for applying the poisson distribution. Thus, the poisson distribution is cheaper to use because the number of accidents is usually recorded by the police department, whereas the total number of drivers is not. www.berrie.dds.nl /poisson.html   (324 words)

 Arizona Rangelands: Inventory and Monitoring: Poisson Distribution Poisson distributions are special sampling distributions generated when discrete individuals are counted from a series of sample units. Poisson distributions are similar to the binomial distribution, except there are more than two alternative outcomes associated with the attribute. Sample data following a Poisson distribution cannot be analyzed using conventional inferential statistical procedures, which assume that data fits a normal distribution. ag.arizona.edu /agnic/az/inventorymonitoring/poisson.html   (163 words)

 Distribution Fitting To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test). The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution. The beta distribution arises from a transformation of the F distribution and is typically used to model the distribution of order statistics. www.statsoft.com /textbook/stdisfit.html   (1769 words)

 CHU - Motivating the Poisson Process in Queuing Models. The appropriateness of the exponential and Poisson distributions, their linkage and their properties which lead to simple analytics, often escape our students as textbooks rarely provide empirical evidence to justify them. Another example is Schmuland (2001), who uses the Poisson model to explain the phenomena of bursts in shark attacks and the scoring patterns of ice hockey legend Wayne Gretzky. Based on his observation that the Poisson distribution provides a good fit for goals scored in ice hockey games, Berry (2000) assumes an exponential distribution for the times between goals to estimate the strategic time to “pull the goalie” when a team is down in a game. ite.pubs.informs.org /Vol3No2/Chu/index.php   (2484 words)

 Poisson distribution   (Site not responding. Last check: ) The poisson distribution is an appropriate model for count data. The poisson distribution was derived by the french mathematician Poisson in 1837, and the first application was the describtion of the number of death by horse kicking in the prussian army (Bortkiewicz, 1898). The poisson distribution is a mathematical rule that assigns probabilities to the number occurences. www.stattucino.com /berrie/poisson.html   (229 words)

 Poisson and Negative Binomial Regression This test tests equality of the mean and the variance imposed by the Poisson distribution against the alternative that the variance exceeds the mean. Poisson Regression Overview, that is, the log of the mean, m, is a linear function of independent variables, Instead of assuming as before that the distribution of  Y, number of occurrences of an event, is Poisson, we will now assume that Y has a negative binomial distribution. www.uky.edu /ComputingCenter/SSTARS/P_NB_3.htm   (741 words)

 PoissonDistributionImpl (Math 1.1 API) Create a new Poisson distribution with the given the mean. Calculates the Poisson distribution function using a normal approximation. distribution is used to approximate the Poisson distribution. jakarta.apache.org /commons/math/api-1.1/org/apache/commons/math/distribution/PoissonDistributionImpl.html   (229 words)

 Normal & Poisson Distribution The normal distribution is symmetric and is used to approximate the binomial distribution when p = q = 1/2. Haldane and Kosambi used the Poisson distribution to adjust the observed number of crossover events to the map distance. A characteristic of the Poisson distribution is that the population mean and variance are equal. www.ag.ndsu.nodak.edu /plantsci/adv_genetics/genetics/np/np02.htm   (174 words)

 [No title]   (Site not responding. Last check: ) The Poisson distribution is used for counting discrete occurrences within a specified time interval. To estimate the number of topological domains, it is assumed that the nicks are introduced in a Poisson distribution (1, 38, 39). Using the Poisson formula, theoretical curves are calculated to determine the best fit with the experimental data points (described in the legend to Fig. www.lycos.com /info/poisson-distribution.html?page=2   (347 words)

 MMU - Research Design, Biol Sci Stats and RDPoisson distribution   (Site not responding. Last check: ) The binomial distribution is used to determine the probability of obtaining a particular number of successes for a binary event. The Poisson distribution is associated with events that have a small probability of occurring. Poisson probabilities are defined by the mean alone since, in a Poisson distribution, µ = s2, (i.e. obelia.jde.aca.mmu.ac.uk /rd/poisson.htm   (313 words)

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