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RESEARCH PRODUCT

Infinitely Divisible Distributions

Achim Klenke

subject

Normal distributionCombinatoricssymbols.namesakesymbolsGamma distributionProbability distributionPoisson distributionConvolution powerInfinite divisibilityStable distributionProbability measureMathematics

description

For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma distribution. In the first section, we study which probability measures on the real line are infinitely divisible and give an exhaustive description of this class of distributions by means of the Levy–Khinchin formula.

yearjournalcountryeditionlanguage
2020-01-01
https://doi.org/10.1007/978-1-4471-5361-0_16