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The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function. [ 1 ] More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n , there exist n i.i.d. random variables X n 1 , ..., X nn whose sum S n = X n 1 + ... + X nn has the ...
Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). One may speak of infinite divisibility, or the lack thereof, of matter , space , time , money , or abstract mathematical objects such as the continuum .
Pages in category "Infinitely divisible probability distributions" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes .
The Cauchy distribution is an infinitely divisible probability distribution. It is also a strictly stable distribution. [8] Like all stable distributions, the location-scale family to which the Cauchy distribution belongs is closed under linear transformations with real coefficients.
Every infinitely divisible probability distribution is a limit of compound Poisson distributions. [1] And compound Poisson distributions is infinitely divisible by the definition. Discrete compound Poisson distribution
All infinitely divisible distributions are a fortiori decomposable; in particular, this includes the stable distributions, such as the normal distribution.; The uniform distribution on the interval [0, 1] is decomposable, since it is the sum of the Bernoulli variable that assumes 0 or 1/2 with equal probabilities and the uniform distribution on [0, 1/2].
An important point about infinitely divisible distributions is their connection to Lévy processes, i.e. at any point in time a Lévy process is infinitely divisibly distributed. Many families of well-known infinitely divisible distributions are so-called convolution-closed, i.e. if the distribution of a Lévy process at one point in time ...
Infinitely divisible probability distributions (1 C, 18 P) L. Location-scale family probability distributions (15 P) N. Noncentral distributions (5 P) P.