Normal Distribution - Revision history

Bradley Monk at 00:34, 28 April 2015

2015-04-28T00:34:58Z

← Older revision		Revision as of 17:34, 27 April 2015
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	\| name = Normal distribution		\| name = Normal distribution
	\| type = density		\| type = density
	\| pdf_image = [[File:~~Normal Distribution PDF~~.~~svg~~\|350px\|Probability density function for the normal distribution]]<br /><small>The red curve is the ''standard normal distribution''</small>		\| 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~~.~~svg~~\|350px\|Cumulative distribution function for the normal distribution]]		\| cdf_image = [[File:Normal_Distribution_CDF.png\|350px\|Cumulative distribution function for the normal distribution]]
	\| notation = ~~<math>\mathcal{N}(\mu,\,\sigma^2)</math>~~		\| notation = [[File:Dist Normal Notation.png]]
	~~\| parameters = {{nowrap\|''μ'' ∈ '''R'''}} — mean (~~[[~~location parameter\|location~~]]~~)<br />{{nowrap\|''σ''<sup>2</sup> > 0}} — variance (squared [[scale parameter\|scale]])~~		\| pdf = [[File:Dist Normal PDF.png]]
	~~\| support = ''x'' ∈ '''R'''~~		\| cdf = [[File:Dist Normal CDF.png]]
	\| pdf = ~~<math>\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}</math>~~		\| quantile = [[File:Dist Normal Quantile.png]]
	\| cdf = ~~<math>\frac12\left~~[~~1 + \operatorname{erf}\left( \frac{x-\mu}{\sigma\sqrt{2}}\right)\right~~] ~~</math>~~		\| mean = µ
	\| quantile = ~~<math>\mu+\sigma\sqrt{2}\,\operatorname{erf}^{-1}(2F-1)</math>~~		\| median = µ
	\| mean = ~~{{math\|''μ''}}~~		\| mode = µ
	\| median = ~~{{math\|''μ''}}~~		\| variance = σ²
	\| mode = ~~{{math\|''μ''}}~~
	\| variance = ~~<math>\sigma^2\,</math>~~
	\| skewness = 0		\| skewness = 0
	\| kurtosis = 0 <!-- DO NOT REPLACE THIS WITH THE OLD-STYLE KURTOSIS WHICH IS 3. -->		\| kurtosis = 0 <!-- DO NOT REPLACE THIS WITH THE OLD-STYLE KURTOSIS WHICH IS 3. -->
	~~\| entropy = <math>\frac12 \ln(2 \pi e \, \sigma^2)</math>~~
	~~\| mgf = <math>\exp\{ \mu t + \frac{1}{2}\sigma^2t^2 \}</math>~~
	~~\| char = <math>\exp \{ i\mu t - \frac{1}{2}\sigma^2 t^2 \}</math>~~
	~~\| fisher = <math>\begin{pmatrix}1/\sigma^2&0\\0&1/(2\sigma^4)\end{pmatrix}</math>~~
	~~\| conjugate prior = Normal distribution~~
	}}		}}

Bradley Monk at 23:46, 27 April 2015

2015-04-27T23:46:11Z

← Older revision		Revision as of 16:46, 27 April 2015
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	f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>&frasl;<sub>2σ ²</sub></sup>		f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>&frasl;<sub>2σ ²</sub></sup>
	</big></big>		</big></big>


			{{Probability distribution
			\| name = Normal distribution
			\| type = density
			\| pdf_image = [[File:Normal Distribution PDF.svg\|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.svg\|350px\|Cumulative distribution function for the normal distribution]]
			\| notation = <math>\mathcal{N}(\mu,\,\sigma^2)</math>
			\| parameters = {{nowrap\|''μ'' ∈ '''R'''}} — mean ([[location parameter\|location]])<br />{{nowrap\|''σ''<sup>2</sup> > 0}} — variance (squared [[scale parameter\|scale]])
			\| support = ''x'' ∈ '''R'''
			\| pdf = <math>\frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x - \mu)^2}{2 \sigma^2}}</math>
			\| cdf = <math>\frac12\left[1 + \operatorname{erf}\left( \frac{x-\mu}{\sigma\sqrt{2}}\right)\right] </math>
			\| quantile = <math>\mu+\sigma\sqrt{2}\,\operatorname{erf}^{-1}(2F-1)</math>
			\| mean = {{math\|''μ''}}
			\| median = {{math\|''μ''}}
			\| mode = {{math\|''μ''}}
			\| variance = <math>\sigma^2\,</math>
			\| skewness = 0
			\| kurtosis = 0 <!-- DO NOT REPLACE THIS WITH THE OLD-STYLE KURTOSIS WHICH IS 3. -->
			\| entropy = <math>\frac12 \ln(2 \pi e \, \sigma^2)</math>
			\| mgf = <math>\exp\{ \mu t + \frac{1}{2}\sigma^2t^2 \}</math>
			\| char = <math>\exp \{ i\mu t - \frac{1}{2}\sigma^2 t^2 \}</math>
			\| fisher = <math>\begin{pmatrix}1/\sigma^2&0\\0&1/(2\sigma^4)\end{pmatrix}</math>
			\| conjugate prior = Normal distribution
			}}

Bradley Monk at 23:36, 8 August 2013

2013-08-08T23:36:01Z

← Older revision		Revision as of 16:36, 8 August 2013
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	[[File:Standard Normal PDF.png\|thumb\|PDF]]		[[File:Standard Normal PDF.png\|thumb\|PDF]]

			[[File:Half Normal Distribution.png\|thumb\|500px\|Half Normal Distribution Equations]]

Bradley Monk at 23:33, 8 August 2013

2013-08-08T23:33:27Z

← Older revision		Revision as of 16:33, 8 August 2013
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	f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>&frasl;<sub>2σ ²</sub></sup>		f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>&frasl;<sub>2σ ²</sub></sup>
	</big></big>		</big></big>


			[[File:Standard Normal Equation.png\|thumb\|Curve Equation]]

			[[File:Standard Normal CDF.png\|thumb\|CDF]]

			[[File:Standard Normal PDF.png\|thumb\|PDF]]

Bradley Monk at 22:37, 3 August 2013

2013-08-03T22:37:38Z

← Older revision		Revision as of 15:37, 3 August 2013
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	<big><big>		<big><big>
	f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ)²</sup>&frasl;<sub>2σ²</sub></sup>		f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ) ²</sup>&frasl;<sub>2σ ²</sub></sup>
	</big></big>		</big></big>


			*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'''.
	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]]

Bradley Monk at 22:22, 3 August 2013

2013-08-03T22:22:24Z

← Older revision		Revision as of 15:22, 3 August 2013
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	<big><big>		<big><big>
	f(x) {{=}} (<sup>1</sup>&frasl;<sub>σ ~~√~~2π </sub>) e<sup>-(<sup>(x-µ)~~<sup>2</sup>~~</sup> &frasl; <sub>2σ~~<sup>2</sup>~~</sub>)</sup>		f(''x'') {{=}} (<sup>1</sup>&frasl;<sub>σ {{math\|{{radical\|2π}}}}</sub>) ''e''<sup>-<sup>(x-µ)²</sup>&frasl;<sub>2σ²</sub></sup>
	</big></big>		</big></big>

Bradley Monk at 22:15, 3 August 2013

2013-08-03T22:15:26Z

← Older revision		Revision as of 15:15, 3 August 2013
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	The normal distribution is		The normal distribution is
	:<~~math~~>
	f(x) ~~= \frac~~{1}{~~\sigma\sqrt{2\pi~~}} e^{ -~~\frac{~~(x-~~\mu~~)^2}{2\sigma^2~~} }.~~		<big><big>
	</~~math~~>		f(x) {{=}} (<sup>1</sup>&frasl;<sub>σ √2π </sub>) e<sup>-(<sup>(x-µ)<sup>2</sup></sup> &frasl; <sub>2σ<sup>2</sup></sub>)</sup>
			</big></big>


	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'''.		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'''.

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	[[File:Cumulative Density Function.png]]		[[File:Cumulative Density Function.png]]





			[[Category:Statistics]]
			[[Category:Math]]
			[[Category:Matlab]]

Bradley Monk: Created page with "The normal distribution is : $f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} }.$ The parameter ''μ'' in this formula is the ''mean'' or ''exp..."

2013-08-03T22:03:34Z

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..."

New page

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 ''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:Probability Density Function.png]]

[[File:Cumulative Density Function.png]]