Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also...

Sn = Xn1 + ... + Xnn has the same distribution F. The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de...

Gottfried Leibniz and Descartes discussed the infinite divisibility of extension. Actual divisibility may be limited due to unavailability of cutting...

x^{2}+t^{2}}\right]} . The distribution of a Lévy process has the property of infinite divisibility: given any integer n, the law of a Lévy process at time t can be...

{\textstyle {\frac {\sigma ^{2}}{n}}} . This property is called infinite divisibility. Conversely, if X 1 {\textstyle X_{1}} and X 2 {\textstyle X_{2}}...

{\displaystyle \log(Z_{s})=\sum _{p\in {\mathcal {P}}}X(p^{-s})\,\log(p)} is infinitely divisible with Lévy measure given by the following sum of Dirac masses: Π s...

\in (0,2]} . The symmetric generalized Gaussian distribution is an infinitely divisible distribution if and only if β ∈ ( 0 , 1 ] ∪ { 2 } {\displaystyle...

"Achilles Paradox", which illustrates the problematic concept of infinite divisibility in space and time. In this paradox, Zeno argues that a swift runner...

parameters, see Mathai or Moschopoulos. The gamma distribution exhibits infinite divisibility. If X ∼ G a m m a ( k , θ ) , {\displaystyle X\sim \mathrm {Gamma}...

1061/(ASCE)0733-9429(1990)116:7(946). Thorin, Olof (1977). "On the infinite divisibility of the lognormal distribution". Scandinavian Actuarial Journal....

In probability theory and statistics, the chi-squared distribution (also chi-square or χ 2 {\displaystyle \chi ^{2}} -distribution) with k {\displaystyle...

{\mu }{n}}+X_{i}-Y_{i}\right)\sim {\textrm {Laplace}}(\mu ,b)} (infinite divisibility) If X has a Laplace distribution, then Y = eX has a log-Laplace...

distribution, we write X ~ Exp(λ). The exponential distribution exhibits infinite divisibility. The cumulative distribution function is given by F ( x ; λ ) =...

identically distributed Bernoulli variables. The Poisson distributions are infinitely divisible probability distributions.: 233 : 164  The directed Kullback–Leibler...

characterization of Poisson point process and infinite divisibility. Sato, Ken-Ito (1999). Lévy processes and infinitely divisible distributions. Cambridge University...

affords a quick way to see that the negative binomial distribution is infinitely divisible. The following recurrence relations hold: For the probability mass...

The Erlang distribution is a two-parameter family of continuous probability distributions with support x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )} ...

'to stand upon or near.' The continuous nature of time and its infinite divisibility was addressed by Aristotle in his Physics, where he wrote on Zeno's...

The Skellam distribution is the discrete probability distribution of the difference N 1 − N 2 {\displaystyle N_{1}-N_{2}} of two statistically independent...

issues demanding proof and, e.g., Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered...

Shalom (2006), "Divisible is injective", Soochow J. Math., 32 (2): 241–243, ISSN 0250-3255, MR 2238765 Griffith, Phillip A. (1970). Infinite Abelian group...

portfolio selection. A random variable Y {\displaystyle Y} is called infinitely divisible if, for each n = 1 , 2 , … {\displaystyle n=1,2,\dots } , there are...

countable set of values, such as the integers, and which are not infinitely divisible. A common method in this form of modelling is to use recurrence relations...

distribution defined on N 0 {\displaystyle \mathbb {N} _{0}} is infinitely divisible, that is, for any positive integer n {\displaystyle n} , there exist...

equal to 0. Cramér's theorem, on decomposing normal distribution Infinite divisibility (probability) Cochran, W. G. (April 1934). "The distribution of...

physics. Physics portal Chemistry portal History of quantum mechanics Infinite divisibility Outline of chemistry Motion Timeline of atomic and subatomic physics...

units −1 and 1 and prime numbers have no non-trivial divisors. There are divisibility rules that allow one to recognize certain divisors of a number from the...

Continuity correction Heavy-tailed distribution Truncated distribution Infinite divisibility Stability (probability) Indecomposable distribution Power law Anderson's...

Every infinitely divisible probability distribution is a limit of compound Poisson distributions. And compound Poisson distributions is infinitely divisible...

equations of electromagnetism, and more generally, the assumption of infinite divisibility of energy in physical systems. Einstein's work predicted that the...