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Discrete probability distribution
probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a given
Poisson_distribution
Probability distribution
can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression.
Negative binomial distribution
Negative_binomial_distribution
Probability distribution
probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials
Poisson_binomial_distribution
Aspect of probability theory
In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random
Compound_Poisson_distribution
Probability distribution
and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William
Conway–Maxwell–Poisson distribution
Conway–Maxwell–Poisson_distribution
Type of random mathematical object
statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of
Poisson_point_process
Compound probability distribution
mixed Poisson distribution is a univariate discrete probability distribution in stochastics. It results from assuming that the conditional distribution of
Mixed_Poisson_distribution
Statistical model for count data
has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression
Poisson_regression
Probability distribution
exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process
Exponential_distribution
to this distribution are a number of other distributions: the displaced Poisson, the hyper-Poisson, the general Poisson binomial and the Poisson type distributions
List of probability distributions
List_of_probability_distributions
statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function
Displaced Poisson distribution
Displaced_Poisson_distribution
Conditional Poisson distribution restricted to positive integers
probability theory, the zero-truncated Poisson distribution (ZTP distribution) is a certain discrete probability distribution whose support is the set of positive
Zero-truncated Poisson distribution
Zero-truncated_Poisson_distribution
Family of continuous probability distributions
the distribution of the time until the kth event of a Poisson process with a rate of λ {\displaystyle \lambda } . The Erlang and Poisson distributions are
Erlang_distribution
Family of probability distributions
distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions that have positive mass at zero, but
Tweedie_distribution
Probability distribution
as B(n + m, p). The binomial distribution is a special case of the Poisson binomial distribution, which is the distribution of a sum of n independent non-identical
Binomial_distribution
probability theory and statistics, the geometric Poisson distribution (also called the Pólya–Aeppli distribution) is used for describing objects that come in
Geometric Poisson distribution
Geometric_Poisson_distribution
French mathematician and physicist (1781–1840)
Baron Siméon Denis Poisson (/pwɑːˈsɒ̃/, US also /ˈpwɑːsɒn/; French: [si.me.ɔ̃ də.ni pwa.sɔ̃]; 21 June 1781 – 25 April 1840) was a French mathematician
Siméon_Denis_Poisson
Probability Theory
rare events or Poisson limit theorem states that the Poisson distribution may be used as an approximation to the binomial distribution, under certain
Poisson_limit_theorem
Compound Poisson distribution Conditional Poisson distribution Conway–Maxwell–Poisson distribution Displaced Poisson distribution Geometric Poisson distribution
List of things named after Siméon Denis Poisson
List_of_things_named_after_Siméon_Denis_Poisson
Probability distribution
distribution or a Poisson distribution – or for that matter, the β of the gamma distribution itself. The closely related inverse-gamma distribution is
Gamma_distribution
Topics referred to by the same term
Tuque, Mauricie, Quebec Poisson distribution, a discrete probability distribution named after Siméon Denis Poisson Poisson's equation, a partial differential
Poisson
Concept in probability theory
our example, if we pick the Gamma distribution as our prior distribution over the rate of the Poisson distributions, then the posterior predictive is
Conjugate_prior
Concept in statistics
probability distributions where the parametrized distribution F {\displaystyle F} is the Poisson distribution is also called mixed Poisson distribution. Mixture
Compound probability distribution
Compound_probability_distribution
same notation to represent the rising factorial.) Suppose X has a Poisson distribution with expected value λ, then its factorial moment generating function
Factorial moment generating function
Factorial_moment_generating_function
Discrete probability distribution
incomplete beta function. A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a
Logarithmic_distribution
Discrete probability distribution
function for the Skellam distribution for a difference K = N 1 − N 2 {\displaystyle K=N_{1}-N_{2}} between two independent Poisson-distributed random variables
Skellam_distribution
Probability distribution
COVID-19. Hypergeometric distribution Coupon collector's problem Compound Poisson distribution Negative binomial distribution Johnson, Norman L.; Kemp
Geometric_distribution
Compound Poisson-family discrete probability distribution
Neyman Type A distribution is a discrete probability distribution from the family of compound Poisson distribution. This distribution can be demonstrated
Neyman_Type_A_distribution
Statistical concept
transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely
Anscombe_transform
mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely
Super-Poissonian_distribution
Definition and first properties of the Poisson-Dirichlet distributions
In probability theory, Poisson-Dirichlet distributions are probability distributions on the set of nonnegative, non-increasing sequences with sum 1, depending
Poisson-Dirichlet distribution
Poisson-Dirichlet_distribution
Family of three random counting measures
only distributions in the canonical non-negative power series family of distributions to possess this property and include the Poisson distribution, negative
Poisson-type_random_measure
Elliptic partial differential equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation
Poisson's_equation
Approximation for factorials
the fact that the Poisson distribution converges to a normal distribution by the Central Limit Theorem. Since the Poisson distribution with parameter μ
Stirling's_approximation
Method used in sports betting
results in 1956. According to his analysis, both Poisson distribution and negative binomial distribution provided an adequate fit to results of football
Statistical association football predictions
Statistical_association_football_predictions
Russian economist and statistician
Polish ancestry. He wrote a book showing how the Poisson distribution, a discrete probability distribution, can be useful in applied statistics, and he made
Ladislaus_Bortkiewicz
Survey methodology process
that the number of samples leads to a Poisson binomial distribution, which can approximate the Poisson distribution (via Le Cam's theorem). Mathematically
Poisson_sampling
Non-informative prior distribution
information about scale. As with the uniform distribution on the reals, it is an improper prior. For the Poisson distribution of the non-negative integer n {\textstyle
Jeffreys_prior
Random process in probability theory
probability distribution. To be precise, a compound Poisson process, parameterised by a rate λ > 0 {\displaystyle \lambda >0} and jump size distribution G, is
Compound_Poisson_process
Expectation or average of the falling factorial of a random variable
]}=n(n-1)(n-2)\cdots (n-r+1)p_{r}} If a random variable X has a Poisson distribution with parameter λ, then the factorial moments of X are E [ ( X )
Factorial_moment
French mathematician (1667–1754)
Univariate Discrete distributions (2nd edition). Wiley. ISBN 0-471-54897-9, p. 157 Stigler, Stephen M. (1982). "Poisson on the poisson distribution". Statistics
Abraham_de_Moivre
Discrete probability distribution
to the way that the Conway–Maxwell–Poisson distribution generalises the Poisson distribution. The CMB distribution can be used to model both positive
Conway–Maxwell–binomial distribution
Conway–Maxwell–binomial_distribution
Orthogonal polynomials
the Hilbert space of square summable sequences associated with the Poisson distribution with parameter μ {\displaystyle \mu } e μ ⟨ C n ( ⋅ , μ ) , C m (
Charlier_polynomials
Topic in probability theory and statistics
are: normal distributions, Poisson distributions, binomial distributions (with common success probability), negative binomial distributions (with common
Relationships among probability distributions
Relationships_among_probability_distributions
Types of wavelets
positive integers, the members of which are associated with the Poisson probability distribution. These wavelets were first defined and studied by Karlene A
Poisson_wavelet
Phenomenon of clustered random events
Denis Poisson, known for his work on definite integrals, electromagnetic theory, and probability theory, and after whom the Poisson distribution is also
Poisson_clumping
Mathematical function for the probability a given outcome occurs in an experiment
hypergeometric distribution Poisson distribution, for the number of occurrences of a Poisson-type event in a given period of time Exponential distribution, for
Probability_distribution
Probability distribution
there is a Zero-truncated Poisson distribution Wikipedia entry. This distribution is the ratio of two Laplace distributions. Let X and Y be standard Laplace
Ratio_distribution
Normalized measure of the dispersion of a probability distribution
between events, or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution. In this context, the observed dataset
Index_of_dispersion
hypothesis that the population from which this sample was taken follows a Poisson distribution. value frequency 0 1 1 2 2 4 3 5 4 3 5 3 6 1 7 0 8 1 > 8 0 {\displaystyle
Minimum_chi-square_estimation
Topics referred to by the same term
In mathematics, the Poisson formula, named after Siméon Denis Poisson, may refer to: Poisson distribution in probability Poisson summation formula in Fourier
Poisson_formula
Presence of greater variability in a data set than would be expected
simple parametric models, such as those based on the Poisson distribution. The Poisson distribution has one free parameter and does not allow for the variance
Overdispersion
Theorem in probability theory
\xi _{2}} has a Poisson distribution, then their sum ξ = ξ 1 + ξ 2 {\displaystyle \xi =\xi _{1}+\xi _{2}} has a Poisson distribution as well. It turns
Raikov's_theorem
Inventory theory process
(X)}}={\sqrt {\ell \sigma _{D}^{2}+d^{2}\sigma _{L}^{2}}}} if demand is Poisson distributed: σ = ℓ σ D 2 + d 2 σ L 2 = θ + d 2 σ L 2 {\displaystyle \sigma
(Q,r)_model
Computer simulation with random inputs
0.375). A poisson process is a process where events occur randomly in an interval of time or space. The probability distribution for Poisson processes
Stochastic_simulation
There are many functions of data distribution. For example, normal distribution, Bernoulli distribution, Poisson distribution, etc. Tu, Jun; Zhou, Guofu (2004)
Data_generating_process
Probability distribution for branching processes
common offspring distribution Poisson with mean μ, then the total number of individuals in the branching process has Borel distribution with parameter μ
Borel_distribution
Collection of random variables
mathematical object. The Poisson process is named after Siméon Poisson, due to its definition involving the Poisson distribution, but Poisson never studied the
Stochastic_process
Probability distribution
Approximation to Poisson Distribution". Stat.ucla.edu. Retrieved March 3, 2017. Bryc (1995, p. 27) Weisstein, Eric W. "Normal Product Distribution". MathWorld
Normal_distribution
Type of control chart in statistical quality control
accounts for quality characteristics that are better modeled by the Poisson distribution. The chart monitors only the process mean; monitoring the process
EWMA_chart
Topics referred to by the same term
Small Numbers, a book by Ladislaus Bortkiewicz Poisson distribution, the use of that name for this distribution originated in the book The Law of Small Numbers
Law_of_small_numbers
stable distribution is the special case of the Poisson distribution. It is the only discrete-stable distribution for which the mean and all higher-order moments
Discrete-stable_distribution
circuit board Monitoring the number of product returns per day The Poisson distribution is the basis for the chart and requires the following assumptions:
C-chart
Observation far apart from others in statistics and data science
given distribution, the number of outliers will follow a binomial distribution with parameter p, which can generally be well-approximated by the Poisson distribution
Outlier
Estimated recurrence time of an event
be similar under both the Poisson and binomial interpretations. The probability mass function of the Poisson distribution is P ( r ; t ) = ( μ t ) r
Return_period
Erroneously seeing patterns in randomness
(Gestalt psychology) List of cognitive biases Numeracy bias Poisson clumping Poisson distribution Statistical randomness Gilovich, Thomas (1991). How we know
Clustering_illusion
Statistical model allowing for frequent zero values
the distribution of the counts is often represented using a Poisson distribution or a negative binomial distribution. Hilbe notes that "Poisson regression
Zero-inflated_model
Generating pseudo-random numbers that follow a probability distribution
normal distribution: Box–Muller transform Marsaglia polar method For generating a Poisson distribution: See Poisson distribution#Generating Poisson-distributed
Non-uniform random variate generation
Non-uniform_random_variate_generation
Probability distribution in actuarial science
negative binomial distribution with a Poisson distribution. Just as the negative binomial distribution can be viewed as a Poisson distribution where the mean
Delaporte_distribution
Set of quantities in probability theory
of the binomial distributions explains the name 'negative binomial distribution'. The limiting case r → +∞ is a Poisson distribution. Introducing the
Cumulant
Topics referred to by the same term
Poisson number can refer to: In mechanics, the reciprocal of Poisson's ratio. 1 / v. In statistics, a number drawn from a Poisson distribution This disambiguation
Poisson_number
Specific quantum state of a quantum harmonic oscillator
coherent states are distributed according to a Poisson distribution. In the case of a Poisson distribution, the variance is equal to the mean, i.e. V a
Coherent_state
Type of control chart
of accidents for delivery trucks per day As with the c-chart, the Poisson distribution is the basis for the chart and requires the same assumptions. The
U-chart
Table used in risk modelling
events in a YLT is the Poisson distribution with constant parameters. An alternative frequency model is the mixed Poisson distribution, which allows for the
Year_loss_table
Probability distribution modeling a coin toss which need not be fair
statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which
Bernoulli_distribution
Type of probability distribution
discrete distributions, examples are the Poisson distribution and the negative binomial distribution (and hence the geometric distribution also). The
Infinite divisibility (probability)
Infinite_divisibility_(probability)
Fourth standardized moment in statistics
Student's t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution. Such distributions
Kurtosis
Probability model of random scattering
implies that the number of points in a fixed region will follow a Poisson distribution. Let there exist a chance process realized by a set of points (called
Poisson_scatter_theorem
Model describing formation of point patterns
offspring from each parent is determined by a probability distribution, such as the Poisson distribution. These offspring points are the observable elements
Neyman–Scott_process
Discrete probability distribution
P o i s ( λ ) {\displaystyle \mathrm {Pois} (\lambda )\,} is the Poisson distribution. lim n → ∞ B e t a B i n ( n , 1 , n p ( 1 − p ) ) ∼ G e o m ( p
Beta-binomial_distribution
Approximation in mathematics
discrete distributions supported on the integers are approximated by the normal distribution. For example, if X has a Poisson distribution with expected
Continuity_correction
Statistical measure of how far values spread from their average
\left[X\right])^{2}} which follows from the law of total variance. If N has a Poisson distribution, then E [ N ] = Var ( N ) {\displaystyle \operatorname {E} [N]=\operatorname
Variance
Statistical theorem
is often enormous. Phone calls arrive at a switchboard according to a Poisson process at an average rate of λ per minute. This rate is not observable
Rao–Blackwell_theorem
Term in probability theory
retrieved through the Conway–Maxwell–Poisson distribution. Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship
(a,b,0) class of distributions
(a,b,0)_class_of_distributions
Special case which arises when input values are at their extremes
case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable
Limiting_case_(mathematics)
Bayesian statistical inference method
(conditional on θ i {\displaystyle \theta _{i}} ) is specified by a Poisson distribution, p ( y i ∣ θ i ) = θ i y i e − θ i y i ! {\displaystyle p(y_{i}\mid
Empirical_Bayes_method
Statistical principle
(\alpha \,,\,\beta )} . If X1, ...., Xn are independent and have a Poisson distribution with parameter λ, then the sum T(X) = X1 + ... + Xn is a sufficient
Sufficient_statistic
Description of the behaviour of bosons
N is always 0. (In contrast, classical particles have instead a Poisson distribution in particle number for a given state, with a much smaller uncertainty
Bose–Einstein_statistics
Product of numbers from 1 to n
chained hash tables, where the distribution of keys per cell can be accurately approximated by a Poisson distribution. Moreover, factorials naturally
Factorial
Numbers parameterizing ways to partition a set
\log n-n+O(n\log \log n/\log n).} If X is a random variable with a Poisson distribution with expected value λ, then its n-th moment is E ( X n ) = ∑ k =
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Class of statistical models
distribution in an exponential family, a large class of probability distributions that includes the normal, binomial, Poisson and gamma distributions
Generalized_linear_model
Generalized Poisson distribution on a locally compact Abelian group, along with the Gaussian distribution, plays an important role in the arithmetic of
Generalized Poisson distribution on a locally compact Abelian group
Generalized_Poisson_distribution_on_a_locally_compact_Abelian_group
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
Robbins_lemma
Probability that random variable X is less than or equal to x
distinction is important for discrete distributions. The proper use of tables of the binomial and Poisson distributions depends upon this convention. Moreover
Cumulative distribution function
Cumulative_distribution_function
Type of electronic noise
Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics, shot noise originates from the discrete nature
Shot_noise
Probability distribution
Wigner distribution is sometimes called the Sato–Tate distribution. See Sato–Tate conjecture. Marchenko–Pastur distribution or Free Poisson distribution Anderson
Wigner semicircle distribution
Wigner_semicircle_distribution
American mathematician
equations. The Thorndike nomogram, a two-dimensional diagram of the Poisson distribution, is named for her. Frances Cope was born in New York City to Elizabeth
Frances_Cope
Type of polynomial sequence
curious connection with the Poisson distribution: If X {\displaystyle X} is a random variable with a Poisson distribution with expected value λ {\displaystyle
Binomial_type
Ratio of infecting agents to infection targets
calculated for a given population using a Poisson distribution. This application of Poisson's distribution was applied and described by Ellis and Delbrück
Multiplicity_of_infection
Algebraic expansion of powers of a binomial
closely related to the probability mass function of the negative binomial distribution. The probability of a (countable) collection of independent Bernoulli
Binomial_theorem
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