Editing Rayleigh distribution (section)

== Applications ==

An application of the estimation of σ can be found in [[magnetic resonance imaging]] (MRI). As MRI images are recorded as [[complex numbers|complex]] images but most often viewed as magnitude images, the background data is Rayleigh distributed. Hence, the above formula can be used to estimate the noise variance in an MRI image from background data.<ref>{{cite journal | last1 = Sijbers | first1 = J. | last2 = den Dekker | first2 = A. J. | last3 = Raman | first3 = E. | last4 = Van Dyck | first4 = D. | year = 1999 | title = Parameter estimation from magnitude MR images | journal = International Journal of Imaging Systems and Technology | volume = 10 | issue = 2| pages = 109–114 | doi=10.1002/(sici)1098-1098(1999)10:2<109::aid-ima2>3.0.co;2-r| citeseerx = 10.1.1.18.1228 }}</ref>
<ref>{{cite journal | last1 = den Dekker | first1 = A. J. | last2 = Sijbers | first2 = J. | year = 2014 | title = Data distributions in magnetic resonance images: a review | journal = Physica Medica | volume = 30 | issue = 7| pages = 725–741 | doi=10.1016/j.ejmp.2014.05.002| pmid = 25059432 }}</ref> 

The Rayleigh distribution was also employed in the field of [[nutrition]] for linking [[Diet (nutrition)|dietary]] [[nutrient]] levels and [[human]] and [[Animal husbandry|animal]] responses. In this way, the [[parameter]] σ may be used to calculate nutrient response relationship.<ref>{{Cite journal|last=Ahmadi|first=Hamed|date=2017-11-21|title=A mathematical function for the description of nutrient-response curve|journal=PLOS ONE|volume=12|issue=11|pages=e0187292|doi=10.1371/journal.pone.0187292|pmid=29161271|issn=1932-6203|bibcode=2017PLoSO..1287292A|pmc=5697816|doi-access=free}}</ref>

In the field of [[ballistics]], the Rayleigh distribution is used for calculating the [[circular error probable]]—a measure of a gun's precision.

In [[physical oceanography]], the distribution of [[significant wave height]] approximately follows a Rayleigh distribution.<ref>{{Cite web|title=Rayleigh Probability Distribution Applied to Random Wave Heights|url=https://www.usna.edu/NAOE/_files/documents/Courses/EN330/Rayleigh-Probability-Distribution-Applied-to-Random-Wave-Heights.pdf|publisher=United States Naval Academy}}</ref>