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Poisson distribution, the Glossary

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.^[1]

169 relations: Abraham de Moivre, Acetylcholine, Addison-Wesley, Admissible decision rule, Agner Krarup Erlang, Anscombe transform, Astronomy, Average absolute deviation, Bayesian inference, Bernoulli distribution, Bernoulli trial, Bias of an estimator, Binomial distribution, Biology, C (programming language), Call centre, Cambridge University Press, Causal sets, Cell (biology), Chemistry, Chernoff bound, Coefficient of variation, Coherent state, Completeness (statistics), Compound Poisson distribution, Compound Poisson process, Confidence interval, Conjugate prior, Continuity correction, Conway–Maxwell–Poisson distribution, Correlation, Count data, Coverage probability, Cramér–Rao bound, Cumulant, Cumulative distribution function, Data transformation (statistics), Discrete-stable distribution, DNA, Dobiński's formula, Donald Knuth, E (mathematical constant), Electric current, Event (probability theory), Exact statistics, Expected value, Exponential function, Factorial, Factorial moment, Financial services, ... Expand index (119 more) »
1711 introductions
Abraham de Moivre
Conjugate prior distributions
Infinitely divisible probability distributions

Abraham de Moivre

Abraham de Moivre FRS (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

See Poisson distribution and Abraham de Moivre

Acetylcholine

Acetylcholine (ACh) is an organic compound that functions in the brain and body of many types of animals (including humans) as a neurotransmitter.

See Poisson distribution and Acetylcholine

Addison-Wesley

Addison–Wesley is an American publisher of textbooks and computer literature.

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Admissible decision rule

In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below.

See Poisson distribution and Admissible decision rule

Agner Krarup Erlang

Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory.

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Anscombe transform

In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution.

See Poisson distribution and Anscombe transform

Astronomy

Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos.

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Average absolute deviation

The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point.

See Poisson distribution and Average absolute deviation

Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

See Poisson distribution and Bayesian inference

Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q. Poisson distribution and Bernoulli distribution are conjugate prior distributions.

See Poisson distribution and Bernoulli distribution

Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

See Poisson distribution and Bernoulli trial

Bias of an estimator

In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated.

See Poisson distribution and Bias of an estimator

Binomial distribution

In probability theory and statistics, the binomial distribution with parameters and is the discrete probability distribution of the number of successes in a sequence of independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability) or failure (with probability). Poisson distribution and binomial distribution are conjugate prior distributions and factorial and binomial topics.

See Poisson distribution and Binomial distribution

Biology

Biology is the scientific study of life.

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C (programming language)

C (pronounced – like the letter c) is a general-purpose programming language.

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Call centre

A call centre (Commonwealth spelling) or call center (American spelling; see spelling differences) is a managed capability that can be centralised or remote that is used for receiving or transmitting a large volume of enquiries by telephone.

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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Causal sets

The causal sets program is an approach to quantum gravity.

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Cell (biology)

The cell is the basic structural and functional unit of all forms of life.

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Chemistry

Chemistry is the scientific study of the properties and behavior of matter.

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Chernoff bound

In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function.

See Poisson distribution and Chernoff bound

Coefficient of variation

In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.

See Poisson distribution and Coefficient of variation

Coherent state

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator.

See Poisson distribution and Coherent state

Completeness (statistics)

In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset.

See Poisson distribution and Completeness (statistics)

Compound Poisson distribution

In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. Poisson distribution and compound Poisson distribution are infinitely divisible probability distributions.

See Poisson distribution and Compound Poisson distribution

Compound Poisson process

A compound Poisson process is a continuous-time stochastic process with jumps.

See Poisson distribution and Compound Poisson process

Confidence interval

Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated.

See Poisson distribution and Confidence interval

Conjugate prior

In Bayesian probability theory, if, given a likelihood function p(x \mid \theta), the posterior distribution p(\theta \mid x) is in the same probability distribution family as the prior probability distribution p(\theta), the prior and posterior are then called conjugate distributions with respect to that likelihood function and the prior is called a conjugate prior for the likelihood function p(x \mid \theta). Poisson distribution and conjugate prior are conjugate prior distributions.

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Continuity correction

In mathematics, a continuity correction is an adjustment made when a discrete object is approximated using a continuous object.

See Poisson distribution and Continuity correction

Conway–Maxwell–Poisson distribution

In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.

See Poisson distribution and Conway–Maxwell–Poisson distribution

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.

See Poisson distribution and Correlation

Count data

In statistics, count data is a statistical data type describing countable quantities, data which can take only the counting numbers, non-negative integer values, and where these integers arise from counting rather than ranking.

See Poisson distribution and Count data

Coverage probability

In statistical estimation theory, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest.

See Poisson distribution and Coverage probability

Cramér–Rao bound

In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter.

See Poisson distribution and Cramér–Rao bound

Cumulant

In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.

See Poisson distribution and Cumulant

Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow satisfying \lim_F(x).

See Poisson distribution and Cumulative distribution function

Data transformation (statistics)

In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point zi is replaced with the transformed value yi.

See Poisson distribution and Data transformation (statistics)

Discrete-stable distribution

The discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution under appropriate scaling is distributed according to the same family.

See Poisson distribution and Discrete-stable distribution

DNA

Deoxyribonucleic acid (DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix.

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Dobiński's formula

In combinatorial mathematics, Dobiński's formula states that the n-th Bell number Bn (i.e., the number of partitions of a set of size n) equals where e denotes Euler's number.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist and mathematician.

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E (mathematical constant)

The number is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.

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Electric current

An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space.

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Exact statistics

Exact statistics, such as that described in exact test, is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating procedures based on asymptotic and approximate statistical methods.

See Poisson distribution and Exact statistics

Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

See Poisson distribution and Expected value

Exponential function

The exponential function is a mathematical function denoted by f(x).

See Poisson distribution and Exponential function

Factorial

In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &. Poisson distribution and factorial are factorial and binomial topics.

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Factorial moment

In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable. Poisson distribution and factorial moment are factorial and binomial topics.

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Financial services

Financial services are economic services tied to finance provided by financial institutions.

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Floor and ceiling functions

In mathematics, the floor function is the function that takes as input a real number, and gives as output the greatest integer less than or equal to, denoted or.

See Poisson distribution and Floor and ceiling functions

Fortran

Fortran (formerly FORTRAN) is a third generation, compiled, imperative programming language that is especially suited to numeric computation and scientific computing.

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France

France, officially the French Republic, is a country located primarily in Western Europe.

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Free convolution

Free convolution is the free probability analog of the classical notion of convolution of probability measures.

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Free independence

In the mathematical theory of free probability, the notion of free independence was introduced by Dan Voiculescu.

See Poisson distribution and Free independence

Free probability

Free probability is a mathematical theory that studies non-commutative random variables.

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Gamma distribution

In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. Poisson distribution and gamma distribution are conjugate prior distributions, factorial and binomial topics and infinitely divisible probability distributions.

See Poisson distribution and Gamma distribution

Gamma function

In mathematics, the gamma function (represented by, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers.

See Poisson distribution and Gamma function

Generating function

In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Poisson distribution and generating function are Abraham de Moivre.

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GNU Scientific Library

The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science.

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Guinness

Guinness is a stout that originated in the brewery of Arthur Guinness at St. James's Gate, Dublin, Ireland, in the 18th century.

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Hermite distribution

In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter.

See Poisson distribution and Hermite distribution

Incomplete gamma function

In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals.

See Poisson distribution and Incomplete gamma function

Independence (probability theory)

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

See Poisson distribution and Independence (probability theory)

Index of dispersion

In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.

See Poisson distribution and Index of dispersion

Infinite divisibility (probability)

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed (i.i.d.) random variables. Poisson distribution and infinite divisibility (probability) are infinitely divisible probability distributions.

See Poisson distribution and Infinite divisibility (probability)

International Agency for Research on Cancer

The International Agency for Research on Cancer (IARC; Centre International de Recherche sur le Cancer, CIRC) is an intergovernmental agency forming part of the World Health Organization of the United Nations.

See Poisson distribution and International Agency for Research on Cancer

Inverse transform sampling

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function.

See Poisson distribution and Inverse transform sampling

Ion channel

Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore.

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Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.

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Journal of the Royal Statistical Society

The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.

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Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution is different from a second, reference probability distribution.

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Ladislaus Bortkiewicz

Ladislaus Josephovich Bortkiewicz (Russian Владислав Иосифович Борткевич, German Ladislaus von Bortkiewicz or Ladislaus von Bortkewitsch) (7 August 1868 – 15 July 1931) was a Russian economist and statistician of Polish ancestry.

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Large number of rare events

In statistics, large number of rare events (LNRE) modeling summarizes methods that allow improvements in frequency distribution estimation over the maximum likelihood estimation when "rare events are common".

See Poisson distribution and Large number of rare events

Lévy metric

In mathematics, the Lévy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables.

See Poisson distribution and Lévy metric

Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.

See Poisson distribution and Limit (mathematics)

Living polymerization

In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed.

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Luria–Delbrück experiment

The Luria–Delbrück experiment (1943) (also called the Fluctuation Test) demonstrated that in bacteria, genetic mutations arise in the absence of selective pressure rather than being a response to it.

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Management

Management (or managing) is the administration of organizations, whether they are a business, a nonprofit organization, or a government body through business administration, nonprofit management, or the political science sub-field of public administration respectively.

See Poisson distribution and Management

Marchenko–Pastur distribution

In the mathematical theory of random matrices, the Marchenko–Pastur distribution, or Marchenko–Pastur law, describes the asymptotic behavior of singular values of large rectangular random matrices.

See Poisson distribution and Marchenko–Pastur distribution

Mathematika

Mathematika is a peer-reviewed mathematics journal that publishes both pure and applied mathematical articles.

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MATLAB

MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.

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Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions.

See Poisson distribution and Maximum entropy probability distribution

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.

See Poisson distribution and Maximum likelihood estimation

Mean

A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers.

See Poisson distribution and Mean

Membrane potential

Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell.

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Microsoft Excel

Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.

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Minimax estimator

In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) \theta \in \Theta from observations x \in \mathcal, an estimator (estimation rule) \delta^M \,\! is called minimax if its maximal risk is minimal among all estimators of \theta \,\!.

See Poisson distribution and Minimax estimator

Minimum-variance unbiased estimator

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.

See Poisson distribution and Minimum-variance unbiased estimator

Mixed Poisson distribution

A mixed Poisson distribution is a univariate discrete probability distribution in stochastics.

See Poisson distribution and Mixed Poisson distribution

Mode (statistics)

In statistics, the mode is the value that appears most often in a set of data values.

See Poisson distribution and Mode (statistics)

Molar mass distribution

In polymer chemistry, the molar mass distribution (or molecular weight distribution) describes the relationship between the number of moles of each polymer species and the molar mass of that species.

See Poisson distribution and Molar mass distribution

Moment (mathematics)

In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.

See Poisson distribution and Moment (mathematics)

Multinomial distribution

In probability theory, the multinomial distribution is a generalization of the binomial distribution. Poisson distribution and multinomial distribution are factorial and binomial topics.

See Poisson distribution and Multinomial distribution

Multiplicity of infection

In microbiology, the multiplicity of infection or MOI is the ratio of agents (e.g. phage or more generally virus, bacteria) to infection targets (e.g. cell).

See Poisson distribution and Multiplicity of infection

Mutation

In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA.

See Poisson distribution and Mutation

Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.

See Poisson distribution and Natural number

Negative binomial distribution

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted r) occurs. Poisson distribution and negative binomial distribution are factorial and binomial topics and infinitely divisible probability distributions.

See Poisson distribution and Negative binomial distribution

Non-uniform random variate generation

Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution.

See Poisson distribution and Non-uniform random variate generation

Normal distribution

In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. Poisson distribution and normal distribution are conjugate prior distributions.

See Poisson distribution and Normal distribution

Optics

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Partition of a set

In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.

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Patrick X. Gallagher

Patrick Ximenes Gallagher (January 2, 1935 – March 30, 2019) was an American mathematician who pioneered large sieve theory and invented the larger sieve.

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Philosophical Transactions of the Royal Society

Philosophical Transactions of the Royal Society is a scientific journal published by the Royal Society.

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Photon

A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

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Poisson clumping

Poisson clumping, or Poisson bursts, is a phenomenon where random events may appear to occur in clusters, clumps, or bursts.

See Poisson distribution and Poisson clumping

Poisson limit theorem

In probability theory, the law of rare events or Poisson limit theorem states that the Poisson distribution may be used as an approximation to the binomial distribution, under certain conditions.

See Poisson distribution and Poisson limit theorem

Poisson point process

In probability theory, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another.

See Poisson distribution and Poisson point process

Poisson regression

In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables.

See Poisson distribution and Poisson regression

Poisson sampling

In survey methodology, Poisson sampling (sometimes denoted as PO sampling) is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample.

See Poisson distribution and Poisson sampling

Poisson wavelet

In mathematics, in functional analysis, several different wavelets are known by the name Poisson wavelet.

See Poisson distribution and Poisson wavelet

Posterior predictive distribution

In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values.

See Poisson distribution and Posterior predictive distribution

Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

See Poisson distribution and Prime number

Probabilistic number theory

In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions.

See Poisson distribution and Probabilistic number theory

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

See Poisson distribution and Probability density function

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

See Poisson distribution and Probability distribution

Probability mass function

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a discrete random variable is exactly equal to some value.

See Poisson distribution and Probability mass function

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability.

See Poisson distribution and Probability theory

Probability-generating function

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable.

See Poisson distribution and Probability-generating function

Prussia

Prussia (Preußen; Old Prussian: Prūsa or Prūsija) was a German state located on most of the North European Plain, also occupying southern and eastern regions.

See Poisson distribution and Prussia

Quantile function

In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value.

See Poisson distribution and Quantile function

Quantum harmonic oscillator

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.

See Poisson distribution and Quantum harmonic oscillator

Quantum key distribution

Quantum key distribution (QKD) is a secure communication method that implements a cryptographic protocol involving components of quantum mechanics.

See Poisson distribution and Quantum key distribution

Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.

See Poisson distribution and Quantum mechanics

Quantum optics

Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules.

See Poisson distribution and Quantum optics

Queueing theory

Queueing theory is the mathematical study of waiting lines, or queues.

See Poisson distribution and Queueing theory

R (programming language)

R is a programming language for statistical computing and data visualization.

See Poisson distribution and R (programming language)

Radioactive decay

Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation.

See Poisson distribution and Radioactive decay

Raikov's theorem

Raikov’s theorem, named for Russian mathematician Dmitrii Abramovich Raikov, is a result in probability theory.

See Poisson distribution and Raikov's theorem

Random matrix

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution.

See Poisson distribution and Random matrix

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

See Poisson distribution and Random variable

Random variate

In probability and statistics, a random variate or simply variate is a particular outcome or ''realization'' of a random variable; the random variates which are other outcomes of the same random variable might have different values (random numbers).

See Poisson distribution and Random variate

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

See Poisson distribution and Real number

Rejection sampling

In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution.

See Poisson distribution and Rejection sampling

Renewal theory

Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times.

See Poisson distribution and Renewal theory

Robbins lemma

In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and f is any function for which the expected value E(f(X)) exists, then Robbins introduced this proposition while developing empirical Bayes methods.

See Poisson distribution and Robbins lemma

Scale parameter

In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions.

See Poisson distribution and Scale parameter

SciPy

SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing.

See Poisson distribution and SciPy

Second Hardy–Littlewood conjecture

In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals.

See Poisson distribution and Second Hardy–Littlewood conjecture

Seismology

Seismology (from Ancient Greek σεισμός (seismós) meaning "earthquake" and -λογία (-logía) meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic waves through the Earth or other planetary bodies.

See Poisson distribution and Seismology

Shape parameter

In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributions that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).

See Poisson distribution and Shape parameter

Shot noise

Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process.

See Poisson distribution and Shot noise

Silver

Silver is a chemical element; it has symbol Ag (derived from Proto-Indo-European ''*h₂erǵ'')) and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal. The metal is found in the Earth's crust in the pure, free elemental form ("native silver"), as an alloy with gold and other metals, and in minerals such as argentite and chlorargyrite.

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Siméon Denis Poisson

Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid mechanics.

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Simon Newcomb

Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath.

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Skellam distribution

The Skellam distribution is the discrete probability distribution of the difference N_1-N_2 of two statistically independent random variables N_1 and N_2, each Poisson-distributed with respective expected values \mu_1 and \mu_2. Poisson distribution and Skellam distribution are infinitely divisible probability distributions.

See Poisson distribution and Skellam distribution

Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of.

See Poisson distribution and Special case

Standard deviation

In statistics, the standard deviation is a measure of the amount of variation of a random variable expected about its mean.

See Poisson distribution and Standard deviation

Standard normal deviate

A standard normal deviate is a normally distributed deviate.

See Poisson distribution and Standard normal deviate

Statistics

Statistics (from German: Statistik, "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

See Poisson distribution and Statistics

Stein's example

In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately.

See Poisson distribution and Stein's example

Stieltjes transformation

In mathematics, the Stieltjes transformation of a measure of density on a real interval is the function of the complex variable defined outside by the formula S_(z).

See Poisson distribution and Stieltjes transformation

Stigler's law of eponymy

Stigler's law of eponymy, proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication "Stigler's law of eponymy", states that no scientific discovery is named after its original discoverer.

See Poisson distribution and Stigler's law of eponymy

Stirling numbers of the second kind

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by S(n,k) or \textstyle \left\. Poisson distribution and Stirling numbers of the second kind are factorial and binomial topics.

See Poisson distribution and Stirling numbers of the second kind

Student center

A student center (or student centre) is a type of building found on university and some high school campuses.

See Poisson distribution and Student center

Sufficient statistic

In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset.

See Poisson distribution and Sufficient statistic

Telecommunications

Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information with an immediacy comparable to face-to-face communication.

See Poisson distribution and Telecommunications

The Art of Computer Programming

The Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis.

See Poisson distribution and The Art of Computer Programming

Time

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, and into the future.

See Poisson distribution and Time

Touchard polynomials

The Touchard polynomials, studied by, also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by \left\x^k, where S(n,k).

See Poisson distribution and Touchard polynomials

Tweedie distribution

In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous.

See Poisson distribution and Tweedie distribution

V-1 flying bomb

The V-1 flying bomb (Vergeltungswaffe 1 "Vengeance Weapon 1") was an early cruise missile.

See Poisson distribution and V-1 flying bomb

Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

See Poisson distribution and Variance

Variance-stabilizing transformation

In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques.

See Poisson distribution and Variance-stabilizing transformation

Web server

A web server is computer software and underlying hardware that accepts requests via HTTP (the network protocol created to distribute web content) or its secure variant HTTPS.

See Poisson distribution and Web server

William Sealy Gosset

William Sealy Gosset (13 June 1876 – 16 October 1937) was an English statistician, chemist and brewer who served as Head Brewer of Guinness and Head Experimental Brewer of Guinness and was a pioneer of modern statistics.

See Poisson distribution and William Sealy Gosset

Wolfram Mathematica

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages.

See Poisson distribution and Wolfram Mathematica

Zero-inflated model

In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations.

See Poisson distribution and Zero-inflated model

Zero-truncated Poisson distribution

In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers.

See Poisson distribution and Zero-truncated Poisson distribution

References

[1] https://en.wikipedia.org/wiki/Poisson_distribution

Also known as Bortkiewicz distribution, Free Poisson, Free Poisson distribution, Free Poisson law, Poison statistics, Poissan distribution, Poisson Probability Distribution, Poisson distributed, Poisson frequency distribution, Poisson law of large numbers, Poisson probability, Poisson random numbers, Poisson random variable, Poisson random variables, Poisson statistic, Poisson statistics, Poisson-distributed, Poissonian, Poissonian distribution, Poseidon distribution, Pseudo-Poisson distribution.

, Floor and ceiling functions, Fortran, France, Free convolution, Free independence, Free probability, Gamma distribution, Gamma function, Generating function, GNU Scientific Library, Guinness, Hermite distribution, Incomplete gamma function, Independence (probability theory), Index of dispersion, Infinite divisibility (probability), International Agency for Research on Cancer, Inverse transform sampling, Ion channel, Joint probability distribution, Journal of the Royal Statistical Society, Kullback–Leibler divergence, Ladislaus Bortkiewicz, Large number of rare events, Lévy metric, Limit (mathematics), Living polymerization, Luria–Delbrück experiment, Management, Marchenko–Pastur distribution, Mathematika, MATLAB, Maximum entropy probability distribution, Maximum likelihood estimation, Mean, Membrane potential, Microsoft Excel, Minimax estimator, Minimum-variance unbiased estimator, Mixed Poisson distribution, Mode (statistics), Molar mass distribution, Moment (mathematics), Multinomial distribution, Multiplicity of infection, Mutation, Natural number, Negative binomial distribution, Non-uniform random variate generation, Normal distribution, Optics, Partition of a set, Patrick X. Gallagher, Philosophical Transactions of the Royal Society, Photon, Poisson clumping, Poisson limit theorem, Poisson point process, Poisson regression, Poisson sampling, Poisson wavelet, Posterior predictive distribution, Prime number, Probabilistic number theory, Probability density function, Probability distribution, Probability mass function, Probability theory, Probability-generating function, Prussia, Quantile function, Quantum harmonic oscillator, Quantum key distribution, Quantum mechanics, Quantum optics, Queueing theory, R (programming language), Radioactive decay, Raikov's theorem, Random matrix, Random variable, Random variate, Real number, Rejection sampling, Renewal theory, Robbins lemma, Scale parameter, SciPy, Second Hardy–Littlewood conjecture, Seismology, Shape parameter, Shot noise, Silver, Siméon Denis Poisson, Simon Newcomb, Skellam distribution, Special case, Standard deviation, Standard normal deviate, Statistics, Stein's example, Stieltjes transformation, Stigler's law of eponymy, Stirling numbers of the second kind, Student center, Sufficient statistic, Telecommunications, The Art of Computer Programming, Time, Touchard polynomials, Tweedie distribution, V-1 flying bomb, Variance, Variance-stabilizing transformation, Web server, William Sealy Gosset, Wolfram Mathematica, Zero-inflated model, Zero-truncated Poisson distribution.

Poisson distribution, the Glossary

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