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*  Poisson distribution
Compound Poisson distribution Conway-Maxwell-Poisson distribution Erlang distribution Hermite distribution Index of dispersion ... The Poisson distribution is a special case of discrete compound Poisson distribution (or stuttering Poisson distribution) with ... Negative binomial distribution Poisson clumping Poisson point process Poisson regression Poisson sampling Poisson wavelet ... about the Poisson distribution, published in 1898. The Poisson distribution arises as the number of points of a Poisson point ...
*  Free Poisson distribution
... the free Poisson distribution is a counterpart of the Poisson distribution in conventional probability theory. The free Poisson ... Poisson process. The measure associated to the free Poisson law is given by μ = { ( 1 − λ ) δ 0 + ν , if 0 ≤ λ ≤ 1 ν , if λ > 1 ... This definition is analogous to one of the ways in which the classical Poisson distribution is obtained from a (classical) ... We give values of some important transforms of the free Poisson law; the computation can be found in e.g. in the book Lectures ...
*  Geometric Poisson distribution
Poisson distribution Compound Poisson distribution Geometric distribution Johnson, Kotz & Kemp 2005, p. 410. Nuel 2008. Johnson ... In probability theory and statistics, the geometric Poisson distribution (also called the Pólya-Aeppli distribution) is used ... Sherbrooke, C. C. (1968). "Discrete compound Poisson processes and tables of the geometric Poisson distribution". Naval ... Nuel, Grégory (March 2008). "Cumulative distribution function of a geometric Poisson distribution". Journal of Statistical ...
*  Compound Poisson distribution
... distribution Negative binomial distribution Geometric distribution Geometric Poisson distribution Gamma distribution Poisson ... then this compound Poisson distribution is named discrete compound Poisson distribution (or stuttering-Poisson distribution) . ... negative binomial distribution, Geometric Poisson distribution, Neyman type A distribution, Luria-Delbrück distribution in ... Poisson} (\lambda ),} i.e., N is a random variable whose distribution is a Poisson distribution with expected value λ, and that ...
*  Displaced Poisson distribution
In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson ... the Poisson distribution is recovered at r = 0. Here I ( ⋅ , ⋅ ) {\displaystyle I\left(\cdot ,\cdot \right)} is the incomplete ... The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is P ( X = n ) / ... "The displaced Poisson distribution". Journal of the American Statistical Association. 62 (318): 643-654. doi:10.1080/ ...
*  Zero-truncated Poisson distribution
This distribution is also known as the conditional Poisson distribution or the positive Poisson distribution. It is the ... In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose ... Random variables sampled from the Zero-truncated Poisson distribution may be achieved using algorithms derived from Poisson ... Singh, Jagbir (1978). "A characterization of positive Poisson distribution and its application". SIAM Journal on Applied ...
*  Conway-Maxwell-Poisson distribution
More generally, the CMP distribution arises as a limiting distribution of Conway-Maxwell-Poisson binomial distribution . X ∼ ... has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case . ... In probability theory and statistics, the Conway-Maxwell-Poisson (CMP or COM-Poisson) distribution is a discrete probability ... and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and ...
*  Poisson binomial distribution
In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of ... Statistics portal Le Cam's theorem Binomial distribution Poisson distribution Wang, Y. H. (1993). "On the number of successes ... Harremoës, P. (2001). "Binomial and Poisson distributions as maximum entropy distributions" (PDF). IEEE Transactions on ... The ordinary binomial distribution is a special case of the Poisson binomial distribution, when all success probabilities are ...
*  Statistics education
Discrete Probability Distributions; Binomial Distribution; Poisson Distributions; Continuous Probability Distributions; The ... The coverage of "Further Statistics" includes: Continuous Probability Distributions; Estimation; Hypothesis Testing; One Sample ... Normal Distribution; Estimation; Hypothesis Testing; Chi-Squared; Correlation and Regression. ...
*  Rape in India
See also: Poisson distribution. Special Correspondent (27 August 2013). "Majority of rape cases go unreported: MPs". The Hindu ... Shanmugam, Ramalingam (2013). "Informatics about fear to report rapes using bumped-up Poisson model". American Journal of ...
*  Cumulant
The limiting case n−1 = 0 is a Poisson distribution. The negative binomial distributions, (number of failures before n ... The Poisson distributions have ε = 1. The negative binomial distributions have ε = p−1 so that ε > 1. Note the analogy to the ... negative binomial distribution'. The limiting case n−1 = 0 is a Poisson distribution. Introducing the variance-to-mean ratio ε ... stable distributions (related to the Lévy distribution) are examples of distributions for which the power-series expansions of ...
*  Abraham de Moivre
ISBN 0-471-54897-9, p157 Stigler, Stephen M. (1982). "Poisson on the poisson distribution". Statistics & Probability Letters. 1 ... As a result, some authors have argued that the Poisson distribution should bear the name of de Moivre. In 1707 de Moivre ... Some results on the Poisson distribution were first introduced by de Moivre in De Mensura Sortis seu; de Probabilitate Eventuum ... Johnson, N.L., Kotz, S., Kemp, A.W. (1993) Univariate Discrete distributions (2nd edition). Wiley. ...
*  Statistical association football predictions
Double Poisson distribution model (same as Maher (1982)), Bivariate Poisson distribution model that uses generalisation of ... According to his analysis, both Poisson distribution and negative binomial distribution provided an adequate fit to results of ... Poisson ( λ ) Y i , j ∼ Poisson ( μ ) {\displaystyle {\begin{aligned}X_{i,j}&\sim {\text{Poisson}}(\lambda )\\Y_{i,j}&\sim {\ ... Unlike the Poisson model that fits the distribution of scores, the Skellam model fits the difference between home and away ...
*  Clustering illusion
doi:10.1016/0010-0285(72)90016-3. Clarke, R. D. (1946). "An application of the Poisson distribution". Journal of the Institute ... Apophenia Alignments of random points Confirmation bias List of cognitive biases Pareidolia Poisson distribution Statistical ... Clarke originally published in 1946 showed that the impacts of V-2 rockets on London were a close fit to a random distribution ... arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict ...
*  Discrete-stable distribution
... known discrete stable distribution is the Poisson distribution which is a special case as the only discrete-stable distribution ... Stable distribution Poisson distribution Steutel, F. W.; van Harn, K. (1979). "Discrete Analogues of Self-Decomposability and ... The discrete-stable distributions are a class of probability distributions with the property that the sum of several random ... They are the discrete analogue of the continuous-stable distributions. The discrete-stable distributions have been used in ...
*  Ladislaus Bortkiewicz
Some have suggested that the Poisson distribution should have been named the "Bortkiewicz distribution." In political economy, ... In 1898 he published a book about the Poisson distribution, titled The Law of Small Numbers. In this book he first noted that ... Bortkiewicz showed that those numbers followed a Poisson distribution. The book also examined data on child-suicides. ... Bortkiewicz presents the Poisson distribution. On pages 23-25, Bortkiewicz presents his famous analysis of "4. Beispiel: Die ...
*  1898 in science
Ladislaus Bortkiewicz publishes a book about the Poisson distribution, The Law of Small Numbers, first noting that events with ... On page 1, Bortkiewicz presents the Poisson distribution. On pages 23-25, Bortkiewicz presents his famous analysis of "4. ... low frequency in a large population follow a Poisson distribution even when the probabilities of the events vary. June 23 - ...
*  András Prékopa
A. Prékopa: On the Compound Poisson Distribution, Acta Scientiarum Mathematicarum, 18(1957), 23-28. Prékopa, A., On Additive ... On Composed Poisson Distributions IV. Acta Math. Acad. Sci. Hung., 3(1952), 317-325. A. Prékopa: Mathematical Treatment of the ... Prékopa, A., A. Rényi and K. Urbanik, On the Limiting Distribution of Sums of Independent Random Variables with Values in ...
*  Vector generalized linear model
Another count regression model is the generalized Poisson distribution. Other possible models are the zeta distribution and the ... As a specific rank-1 example of a QRR-VGLM, consider Poisson data with S species. The model for Species s is the Poisson ... When it is not, the resulting quasi-likelihood model is often described as Poisson with overdispersion, or quasi-Poisson; then ... But the VGLM framework readily handles models such as zero-inflated Poisson regression, zero-altered Poisson (hurdle) ...
*  Imaging cycler microscopy
Dress, Andreas W. M.; Lokot, T.; Pustyl'nikov, L. D.; Schubert, W. (January 2005). "Poisson Numbers and Poisson Distributions ...
*  Bias of an estimator
Suppose that X has a Poisson distribution with expectation λ. Suppose it is desired to estimate P ⁡ ( X = 0 ) 2 = e − 2 λ {\ ... A far more extreme case of a biased estimator being better than any unbiased estimator arises from the Poisson distribution. ... and then probability distributions of a statistic are considered, based on the predicted sampling distribution of the data. For ... Xn follow a normal distribution, then nS2/σ2 has a chi-squared distribution with n − 1 degrees of freedom, giving: E ⁡ [ n S 2 ...
*  Index of dispersion
... or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution. In this context, ... Some distributions, most notably the Poisson distribution, have equal variance and mean, giving them a VMR = 1. The geometric ... The first to discuss the use of a test to detect deviations from a Poisson or binomial distribution appears to have been Lexis ... it has a value of one when the probability distribution of the number of occurrences in an interval is a Poisson distribution. ...
*  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 ... which is the OGF for the Poisson distribution. (The second equality holds due to the definition of the Exponential function.) ... approximation to the binomial distribution, under certain conditions. The theorem was named after Siméon Denis Poisson (1781- ... It is also possible to demonstrate the theorem through the use of Ordinary Generating Functions of the binomial distribution: G ...
*  Virus quantification
0.69 TCID50 based on the Poisson distribution, a probability distribution which describes how many random events (virus ... A more precise estimate is obtained by applying the Poisson distribution. Where P(o) is the proportion of negative tubes and m ...
*  Exponential tilting
... the Poisson distribution p ( k ) = e − μ μ k / k ! {\displaystyle p(k)=e^{-\mu }\mu ^{k}/k!} , where p θ {\displaystyle p_{\ ... However, for some distributions, the exponentially tilted distribution does not belong to the same parametric family as f {\ ... of distributions that can be used as proposal distributions for acceptance-rejection sampling or importance distributions for ... Applying the exponentially tilted distribution as the importance distribution yields the equation E ( h ( X ) ) = E θ ( L ( X ...
*  Berry-Esseen theorem
... and Φ the cumulative distribution function of the standard normal distribution, then for all x and n, , F n ( x ) − Φ ( x ... "An improvement of the Berry-Esseen inequality with applications to Poisson and mixed Poisson random sums". Scandinavian ... then the cumulative distribution functions of the standardized sample mean and the standard normal distribution differ ( ... the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size ...