Erf Error Function Wiki
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In other words, Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard erf error function ti-89 deviations above the mean. If the underlying random variable is y,
Excel Error Function Erf
then the proper argument to the tail probability is derived as: x = y − μ
Erf Q Function
σ {\displaystyle x={\frac {y-\mu }{\sigma }}} which expresses the number of standard deviations away from the mean. Other definitions of the Q-function, all of which are simple transformations
Erf Wikipedia
of the normal cumulative distribution function, are also used occasionally.[3] Because of its relation to the cumulative distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics. Contents 1 Definition and basic properties 2 Values 3 Generalization to erf normal distribution high dimensions 4 References Definition and basic properties[edit] Formally, the Q-function is defined as Q ( x ) = 1 2 π ∫ x ∞ exp ( − u 2 2 ) d u . {\displaystyle Q(x)={\frac {1}{\sqrt {2\pi }}}\int _{x}^{\infty }\exp \left(-{\frac {u^{2}}{2}}\right)\,du.} Thus, Q ( x ) = 1 − Q ( − x ) = 1 − Φ ( x ) , {\displaystyle Q(x)=1-Q(-x)=1-\Phi (x)\,\!,} where Φ ( x ) {\displaystyle \Phi (x)} is the cumulative distribution function of the normal Gaussian distribution. The Q-function can be expressed in terms of the error function, or the complementary error function, as[2] Q ( x ) = 1 2 ( 2 π ∫ x / 2 ∞ exp ( − t 2 ) d t ) = 1 2 − 1 2 erf ( x 2 ) -or- = 1 2 erfc ( x 2 ) . {\displaystyle {\begin{aligned}Q(x)&={\frac {1}{2}}\left({\frac {2}{\sqrt {\pi }}}\int _{x/{\sqrt {2}}}^{\infty }\exp \left(-t^{2}\right)\,dt\right)\\&={\frac {1}{2}}-{\fr
France or Reformed Church of France, a denomination in France with Calvinist origins erf erfc Industry[edit] Enerplus, a North American energy producer whose stock is mathematica erf listed as ERF under the TSX and NYSE ERF (truck manufacturer), a British truck manufacturer gaussian erf Science[edit] Error function, a function used in mathematics and statistics ERF (gene), a gene for a human transcription factor Eukaryotic release factors, proteins in https://en.wikipedia.org/wiki/Q-function biology Event-related field, the magnetic equivalent of an event-related potential in functional brain imaging Other[edit] Erfurt-Weimar Airport (IATA Airport Code), the national airport of Erfurt, Germany European Refugee Fund, support for refugees in member states of the European Union Extreme Reaction Force, a type of riot squad in U.S. https://en.wikipedia.org/wiki/ERF military prisons ERF damper, Electrorheological fluid damper This disambiguation page lists articles associated with the title ERF. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from "https://en.wikipedia.org/w/index.php?title=ERF&oldid=730964480" Categories: Disambiguation pagesHidden categories: All article disambiguation pagesAll disambiguation pages Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaWikipedia store Interaction HelpAbout WikipediaCommunity portalRecent changesContact page Tools What links hereRelated changesUpload fileSpecial pagesPermanent linkPage informationWikidata itemCite this page Print/export Create a bookDownload as PDFPrintable version Languages DeutschEestiFrançaisItalianoNederlandsPolski Edit links This page was last modified on 22 July 2016, at 00:39. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and P
error function and complimentary function used in communications are not exactly the same as the ones typically used in statistics. The relationship between the two is given at the http://www.rfcafe.com/references/mathematical/erf-erfc.htm bottom of the page. In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics, materials science, and partial differential equations. "In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics, materials science, and partial differential equations." - Wikipedia error function The Gaussian probability density function with mean = 0 and variance =1 is The error function erf(x) is defined as: Note that erf(0) = 0.5, and that erf(∞)=1. The complimentary error function erfc(x) is defined as: The following graph illustrates the region of the normal curve that is being integrated. For large values of x (>3), the complimentary erf error function error function can be approximated by: The error in the approximation is about -2% for x=3, and -1% for x=4, and gets progressively better with larger values of x. Approximations RF Cafe visitor Ilya L. provided an approximation for the error function and complimentary error function that was published by Sergei Winitzki titled, "A handy approximation for the error function and its inverse." February 6, 2008. Here are the main results: Error function approximation: , where Complimentary error function: NOTE: I used to have an alternative approximation formula for the complimentary error function for large values of x, but decided to remove it since the source for it is not generally available to the public. It can be found as equation #13, on page 641, of IEEE Transactions on Communications volume COM-27, No. 3, dated March 1979. A subscription to the IEEE service is required to access the article. Try Using SEARCH to Find What You Need. >10,000 Pages Indexed on RF Cafe ! Copyright 1996 - 2016Webmaster: Kirt Blattenberger, BSEE - KB3UONFamily Websites: Airplanes and Rockets | Equine Kingdom All trademarks, copyrights, patents, and other rights of owner