Editing Stable distribution (section)

== Applications ==
Stable distributions owe their importance in both theory and practice to the generalization of the [[central limit theorem]] to random variables without second (and possibly first) order [[moment (mathematics)|moments]] and the accompanying [[self-similarity]] of the stable family. It was the seeming departure from normality along with the demand for a self-similar model for financial data (i.e. the shape of the distribution for yearly asset price changes should resemble that of the constituent daily or monthly price changes) that led [[Benoît Mandelbrot]] to propose that cotton prices follow an alpha-stable distribution with <math>\alpha</math> equal to 1.7.<ref name="BM 1963"/> [[Lévy distribution]]s are frequently found in analysis of [[critical behavior]] and financial data.<ref name=":1" /><ref>{{Cite book|title = Stable Paretian Models in Finance|last1 = Rachev|first1 = Svetlozar T.|publisher = Wiley|year = 2000|isbn = 978-0-471-95314-2|url = http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471953148.html|last2 = Mittnik|first2 = Stefan}}</ref>

They are also found in [[spectroscopy]] as a general expression for a quasistatically [[pressure broadening|pressure broadened spectral line]].<ref name=":3" />

The Lévy distribution of solar flare waiting time events (time between flare events) was demonstrated for [[CGRO]] BATSE hard x-ray solar flares in December 2001. Analysis of the Lévy statistical signature revealed that two different memory signatures were evident; one related to the solar cycle and the second whose origin appears to be associated with a localized or combination of localized solar active region effects.<ref>[http://www.library.unt.edu/theses/open/20013/leddon_deborah/dissertation.pdf Leddon, D., A statistical Study of Hard X-Ray Solar Flares]</ref>