About: Infinite divisibility (probability)

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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. The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function. More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n, there exist n i.i.d. random variables Xn1, ..., Xnn whose sum Sn = Xn1 + … + Xnn has the same distribution F.

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rdfs:label	Infinite divisibility (probability) (en)
rdfs:comment	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. The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function. More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n, there exist n i.i.d. random variables Xn1, ..., Xnn whose sum Sn = Xn1 + … + Xnn has the same distribution F. (en)
sameAs	Infinite divisibility (probability) Infinite divisibility (probability)
dbp:wikiPageUsesTemplate	dbt:Doi dbt:Main dbt:ProbDistributions dbt:Reflist
Subject	Theory of probability distributions Types of probability distributions Infinitely divisible probability distributions
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Infinite_divisibility_(probability)?oldid=1072833323&ns=0
Wikipage page ID	13588803 (xsd:integer)
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Wikipage revision ID	1072833323 (xsd:integer)
Link from a Wikipage to another Wikipage	Normal distribution Probability Probability distribution Probability theory Support (mathematics) Theory of probability distributions Additive process Bernoulli distribution Binomial distribution Statistics Bruno de Finetti Cauchy distribution Central limit theorem Geometric distribution Domain of a function Characteristic function (probability theory) Càdlàg Triangular array Compound Poisson distribution Continuous stochastic process Continuous uniform distribution Convergence of random variables Cramér's decomposition theorem Gamma distribution Indecomposable distribution Independence (probability theory) Independent and identically distributed random variables Irrational number Variance Stable distribution Stochastic process Student's t-distribution Independent increments Lévy process Inverse second Negative binomial distribution Poisson distribution Poisson limit theorem Random variable Rational number Types of probability distributions Infinitely divisible probability distributions Stationary increments
has abstract	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. The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function. More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n, there exist n i.i.d. random variables Xn1, ..., Xnn whose sum Sn = Xn1 + … + Xnn has the same distribution F. The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de Finetti. This type of decomposition of a distribution is used in probability and statistics to find families of probability distributions that might be natural choices for certain models or applications. Infinitely divisible distributions play an important role in probability theory in the context of limit theorems. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Infinite_divisibility_(probability)
is Wikipage redirect of	Infinitely divisible distribution Infinitely divisible probability distribution Infinitely divisible process
is Link from a Wikipage to another Wikipage of	List of statistics articles Log-Cauchy distribution Log-normal distribution Normal-inverse Gaussian distribution Normal distribution Additive process Bruno de Finetti Catalog of articles in probability theory Cauchy distribution Generalised hyperbolic distribution Generalized inverse Gaussian distribution Generalized normal distribution Geometric distribution Discrete-stable distribution List of probability topics Cochran's theorem Combinant Compound Poisson distribution Convolution power List of convolutions of probability distributions Mourad Ismail Financial models with long-tailed distributions and volatility clustering Gamma distribution Gausssian distribution on a locally compact Abelian group Indecomposable distribution Exponential distribution Klaus Matthes Laplace distribution Laplace–Stieltjes transform Lévy process Negative binomial distribution Negative multinomial distribution Infinitely divisible distribution Infinitely divisible probability distribution Infinitely divisible process
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Infinite_divisibility_(probability)

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