Q-function: Difference between revisions
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time for this to be an article of its own. further info will be added soon. some of the material was adapted from normal distribution. |
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In statistics, the '''Q-function''' is defined as the [[tail probability]] of the normalized [[Gaussian distribution]]. In other words, <math>Q(x)</math> is the probability that a normalized Gaussian random variable will obtain a value larger than <math>x</math>. |
In statistics, the '''Q-function''' is defined as the [[tail probability]] of the normalized [[Gaussian distribution]].<ref>[http://cnx.org/content/m11537/latest/ The Q-function<!-- Bot generated title -->]</ref><ref>http://www.eng.tau.ac.il/~jo/academic/Q.pdf</ref> In other words, <math>Q(x)</math> is the probability that a normalized Gaussian random variable will obtain a value larger than <math>x</math>. Other definitions of the Q-function, all of which are simple transformations of the normal [[cumulative distribution function]], are also used occasionally.<ref>[http://mathworld.wolfram.com/NormalDistributionFunction.html Normal Distribution Function - from Wolfram MathWorld<!-- Bot generated title -->]</ref> |
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Formally, the Q-function is defined as |
Formally, the Q-function is defined as |
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=\frac{1}{2} - \frac{1}{2} \operatorname{erf} \Bigl( \frac{x}{\sqrt{2}} \Bigr). |
=\frac{1}{2} - \frac{1}{2} \operatorname{erf} \Bigl( \frac{x}{\sqrt{2}} \Bigr). |
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</math> |
</math> |
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== References == |
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<references /> |
Revision as of 07:56, 7 April 2009
In statistics, the Q-function is defined as the tail probability of the normalized Gaussian distribution.[1][2] In other words, is the probability that a normalized Gaussian random variable will obtain a value larger than . Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally.[3]
Formally, the Q-function is defined as
The Q-function can be expressed in terms of the error function as