Stretched exponential function: Difference between revisions

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Correct the integral for the first moment of underlying distribution of time constants
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| doi = 10.1039/tf9706600080
|s2cid=95007734
}}.</ref> in this context, the stretched exponential or its Fourier transform are also called the '''Kohlrausch–Williams–Watts (KWW) function'''. The Kohlrausch–Williams–Watts (KWW) function corresponds to the time ___domain charge response of the main dielectric models, such as the [[Cole-Cole_equation]], the [[Cole-Davidson_equation]], and the [[Havriliak–Negami_relaxation]], for small time arguments.<ref>{{Cite journal |last=Holm|first=Sverre|title=Time ___domain characterization of the Cole-Cole dielectric model |url=https://sciendo.com/article/10.2478/joeb-2020-0015 |journal=Journal of Electrical Bioimpedance |year=2020 |volume=11 |issue=1 |pages=101–105|doi=10.2478/joeb-2020-0015|pmid=33584910 |pmc=7851980 }}</ref>
 
In phenomenological applications, it is often not clear whether the stretched exponential function should be used to describe the differential or the integral distribution function—or neither.
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=== Wireless Communications ===
In wireless communications, a scaled version of the stretched exponential function has been shown to appear in the Laplace Transform for the interference power <math>I</math> when the transmitters' locations are modeled as a 2D [[Poisson point process|Poisson Point Process]] with no exclusion region around the receiver.<ref>{{cite journalbook
| author = Ammar, H. A., Nasser, Y. and Artail, H.
| journaltitle = 2018 IEEE International Conference on Communications (ICC)
| titlechapter = Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks
| year = 2018
| title = Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks
| journal = 2018 IEEE International Conference on Communications (ICC)
| pages = 1–6
| doi = 10.1109/ICC.2018.8422214 | arxiv = 1803.10440 | isbn = 978-1-5386-3180-5