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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 ...
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 .
Pages in category "Types of probability distributions" The following 38 pages are in this category, out of 38 total. ... Infinite divisibility (probability) Inverse ...
Infinite divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma; Characteristic function (probability theory) Lévy continuity theorem; Darmois–Skitovich theorem; Edgeworth series; Helly–Bray theorem; Kac–Bernstein theorem; Location parameter; Maxwell's theorem; Moment-generating function
Barndorff-Nielsen and Halgreen proved that the GIG distribution is infinitely divisible and since the GH distribution can be obtained as a normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian distribution, Barndorff-Nielsen and Halgreen showed the GH distribution is infinitely divisible as well.
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 represented as the law of the sum of n independent random variables, which are precisely the increments of the Lévy process over time intervals of length t/n, which are independent and identically ...
Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability.The classic exposition of his distinctive theory is the 1937 "La prévision: ses lois logiques, ses sources subjectives", [1] which discussed probability founded on the coherence of betting odds and the consequences of ...
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