Normal Distribution: Difference between revisions
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Bradley Monk (talk | contribs) (Created page with "The normal distribution is :<math> f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} }. </math> The parameter ''μ'' in this formula is the ''mean'' or ''exp...") |
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The normal distribution is | The normal distribution is | ||
f(x) = | <big><big> | ||
f(''x'') {{=}} (<sup>1</sup>⁄<sub>σ {{math|{{radical|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>⁄<sub>2σ ²</sub></sup> | |||
The parameter ''μ'' in this formula is the ''mean'' or ''expectation'' of the distribution (and also its median and mode). The parameter ''σ'' is its standard deviation; its variance is therefore σ'<sup> 2</sup>. A random variable with a Gaussian distribution is said to be '''normally distributed''' and is called a '''normal deviate'''. | </big></big> | ||
{{Probability distribution | |||
| name = Normal distribution | |||
| type = density | |||
| pdf_image = [[File:Probability Density Function.png|350px|Probability density function for the normal distribution]]<br /><small>The red curve is the ''standard normal distribution''</small> | |||
| cdf_image = [[File:Normal_Distribution_CDF.png|350px|Cumulative distribution function for the normal distribution]] | |||
| notation = [[File:Dist Normal Notation.png]] | |||
| pdf = [[File:Dist Normal PDF.png]] | |||
| cdf = [[File:Dist Normal CDF.png]] | |||
| quantile = [[File:Dist Normal Quantile.png]] | |||
| mean = µ | |||
| median = µ | |||
| mode = µ | |||
| variance = σ² | |||
| skewness = 0 | |||
| kurtosis = 0 <!-- DO NOT REPLACE THIS WITH THE OLD-STYLE KURTOSIS WHICH IS 3. --> | |||
}} | |||
[[File:Standard Normal Equation.png|thumb|Curve Equation]] | |||
[[File:Standard Normal CDF.png|thumb|CDF]] | |||
[[File:Standard Normal PDF.png|thumb|PDF]] | |||
[[File:Half Normal Distribution.png|thumb|500px|Half Normal Distribution Equations]] | |||
*The parameter ''μ'' in this formula is the ''mean'' or ''expectation'' of the distribution (and also its median and mode). | |||
*The parameter ''σ'' is its standard deviation; its variance is therefore σ'<sup> 2</sup>. A random variable with a Gaussian distribution is said to be '''normally distributed''' and is called a '''normal deviate'''. | |||
[[File:Standard Normal.png]] | [[File:Standard Normal.png]] | ||
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[[File:Cumulative Density Function.png]] | [[File:Cumulative Density Function.png]] | ||
[[Category:Statistics]] | |||
[[Category:Math]] | |||
[[Category:Matlab]] | |||
Latest revision as of 17:34, 27 April 2015
The normal distribution is
f(x) = (1⁄σ √2π) e-(x-µ) ²⁄2σ ²
| Probability density function Error creating thumbnail: File missing The red curve is the standard normal distribution | |
| Cumulative distribution function Error creating thumbnail: File missing | |
| Notation | 
|
|---|---|
| |
| CDF | 
|
| Mean | µ |
| Median | µ |
| Mode | µ |
| Variance | σ² |
| Skewness | 0 |
| Kurtosis | 0 |
- The parameter μ in this formula is the mean or expectation of the distribution (and also its median and mode).
- The parameter σ is its standard deviation; its variance is therefore σ' 2. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
