Synonyms
Lévy skew α-stable distribution
Definition
A random variable Z is said to follow a symmetric α-stable distribution [13, 15], where 0 < α ≤ 2, if the Fourier transform of its probability density function fZ (z) satisfies
where d > 0 is the scale parameter. This is denoted by Z ∼ S(α, d).
There is an equivalent definition. A random variable Z follows a symmetric α-stable distribution if, for any real numbers, C1 and C2,
where Z1 and Z2 are independent copies of Z, and the symbol “\( \overset{d}{=} \)” denotes equality in distribution.
The probability density function fZ (z) can be obtained by taking inverse Fourier transform of 1. In particular, fZ (z) can be expressed in closed-forms when α = 2 (i.e., the normal distribution) and α= 1 (i.e., the...
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Li, P. (2018). Stable Distribution. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_367
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