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###### Poissondistribution
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 Poissondistribution
... 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 Poissondistribution
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 Poissondistribution
... 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 ...
###### 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 ...
###### 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 ...
###### 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 ...
###### 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 ...
###### 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 ...