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en>Earcanal: /* Types */ Delete stray comma.

2015-01-10T18:06:54Z

Types: Delete stray comma.

← Older revision		Revision as of 20:06, 10 January 2015
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	~~Hiya. The author's name is Eusebio but rather he never really enjoyed that name~~. ~~The precious hobby for him and his kids is on to drive and he's found itself doing it for quite~~ a ~~while. Auditing is how he supports my family. Massachusetts is where~~ or ~~even and his [http://wifesurvive~~.~~com/ wife survive]. He's been working~~ in ~~his website~~ for ~~selected time now. Check understand it out here: http://circuspartypanama~~.~~com~~<br><br>		Games can give you your universe of experience, remainder and exhilaration. One might learn, get a good sense of success or in simple terms enjoy beating down unquestionably the bad-guy. No matter what form of video video games you are into, add the helpful tips in such post to give for yourself more fun whenever any person play your next electriconic game Website.<br><br>

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en>Friend of facts2: /* Rank-biserial correlation */ Example to illustrate rank-biserial correlation computations by the Kerby simple difference formula and by the Wendt formula

2014-02-28T13:39:26Z

Rank-biserial correlation: Example to illustrate rank-biserial correlation computations by the Kerby simple difference formula and by the Wendt formula

← Older revision		Revision as of 15:39, 28 February 2014
Line 1:		Line 1:
	~~{{Probability distribution~~		Hiya. The author's name is Eusebio but rather he never really enjoyed that name. The precious hobby for him and his kids is on to drive and he's found itself doing it for quite a while. Auditing is how he supports my family. Massachusetts is where or even and his [http://wifesurvive.com/ wife survive]. He's been working in his website for selected time now. Check understand it out here: http://circuspartypanama.com<br><br>
	\| name ~~=Matrix normal~~
	~~\| type =density~~
	~~\| box_width =195px~~
	~~\| pdf_image =~~
	~~\| cdf_image =~~
	~~\| notation =<math>\mathcal{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math>~~
	~~\| parameters =<math>\mathbf{M}</math>~~ [~~[location parameter\|location]] ([[real number\|real]] <math>n\times p<~~/~~math> [[matrix (mathematics)\|matrix]])<br/>~~
	~~<math>\mathbf{U}<~~/~~math> [[scale matrix\|scale]] ([[positive-definite matrix\|positive-definite]] [[real number\|real]] <math>n\times n<~~/~~math> [[matrix (mathematics)\|matrix~~]~~])<br/>~~
	~~<math>\mathbf{V}</math> [[scale matrix\|scale]] ([[positive-definite matrix\|positive-definite]] [[real number\|real]] <math>p\times p</math> [[matrix (mathematics)\|matrix]])~~
	~~\| support =<math>\mathbf{X} \~~in ~~\mathbb{R}^{n \times p}</math>~~
	~~\| pdf =<math>\frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left[ \mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{T} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np~~/~~2} \|\mathbf{V}\|^{n~~/~~2} \|\mathbf{U}\|^{p/2}}~~<~~/math~~>
	~~\| cdf =~~
	~~\| mean =~~<~~math>\mathbf{M}</math>~~
	~~\| median =~~
	~~\| mode =~~
	~~\| variance =<math>\mathbf{U}</math> (among-row) and <math>\mathbf{V}</math~~> ~~(among-column)~~
	~~\| skewness =~~
	~~\| kurtosis =~~
	~~\| entropy =~~
	~~\| mgf =~~
	~~\| char =~~
	}}

	~~In [[statistics]], the '''matrix normal distribution''' is a [[probability distribution]] that is a generalization of the [[multivariate normal distribution]] to matrix-valued random variables.~~		Also visit my homepage; [http://circuspartypanama.com clash of clans hack download no survey no password]

	~~== Definition ==~~
	~~The [[probability density function]] for the random matrix '''X''' (''n'' ×&nbsp~~;~~''p'') that follows the matrix normal distribution <math>\mathcal{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math> has the form:~~

	~~:<math>~~
	~~p(\mathbf{X}\|\mathbf{M}, \mathbf{U}, \mathbf{V}) = \frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left~~[ ~~\mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{T} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np/2} \|\mathbf{V}\|^{n/2} \|\mathbf{U}\|^{p/2}}~~
	~~</math>~~

	~~where '''M''' is ''n'' × ''p'', '''U''' is ''n'' × ''n'' and '''V''' is ''p'' × ''p''.~~

	~~There are several ways to define the two covariance matrices. One possibility is~~

	:~~<math>\mathbf{U} = E[(\mathbf{X} - \mathbf{M})(\mathbf{X} - \mathbf{M})^{T}]<~~/~~math>~~

	~~:<math>\mathbf{V} = E[(\mathbf{X} - \mathbf{M})^{T} (\mathbf{X} - \mathbf{M})] / c</math>~~

	~~where <math>c</math> is a constant which depends on '''U''' and ensures appropriate power normalization.~~

	~~The matrix normal is related to the [[multivariate normal distribution]] in the following way:~~

	~~:<math>\mathbf{X} \sim \mathcal{MN}_{n\times p}(\mathbf{M}, \mathbf{U}, \mathbf{V}),</math>~~

	~~if and only if~~

	~~:<math>\mathrm{vec}(\mathbf{X}) \sim \mathcal{N}_{np}(\mathrm{vec}(\mathbf{M}), \mathbf{V} \otimes \mathbf{U})</math>~~

	~~where <math>\otimes</math> denotes the [[Kronecker product]] and <math>\mathrm{vec}(\mathbf{M})</math> denotes the [[vectorization (mathematics)\|vectorization]] of <math>\mathbf{M}<~~/~~math>~~.

	~~==Example==~~
	~~Let's imagine a sample~~ of ~~''n'' independent ''p''-dimensional random variables identically distributed according to a [[multivariate normal distribution]]:~~
	~~:<math>\mathbf{Y}_i \sim \mathcal{N}_p({\boldsymbol \mu}, {\boldsymbol \Sigma}) \text{ with } i \in \{1,\ldots,n\}</math>.~~
	~~When defining the ''n'' × ''p'' matrix <math>\mathbf{X}</math> for which the ''i''th row is <math>\mathbf{Y}_i</math>, we obtain:~~
	~~:<math>\mathbf{X} \sim \mathcal{MN}_{n \times p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math>~~
	where each row of <math>\mathbf{M}</math> is equal to <math>{\boldsymbol \mu}</math>, that is <math>\mathbf{M}=\mathbf{1}_n \times {\boldsymbol \mu}^T</math>, <math>\mathbf{U}</math> is the ''n'' × ''n'' identity matrix, that is the rows are independent, and <math>\mathbf{V} = {\boldsymbol \Sigma}</math>.

	~~==Relation to other distributions==~~
	Dawid (1981) provides a discussion of the relation of the matrix-valued normal distribution to other distributions, including the [[Wishart distribution]], [[Inverse Wishart distribution]] and [[matrix t-distribution]], but uses different notation from that employed here.

	~~== See also ==~~
	* [[Multivariate normal distribution]].

	~~==References==~~
	* {{cite journal
	~~\|last=Dawid \|first=A.P. \|authorlink=Philip Dawid~~
	~~\|year=1981~~
	~~\|title=Some matrix-variate distribution theory: Notational considerations and a Bayesian application~~
	~~\|journal=[[Biometrika]]~~
	~~\|volume=68 \|issue=1 \|pages=265–274~~
	~~\|doi=10.1093/biomet/68.1.265 \|mr=614963 \| jstor = 2335827~~
	}}
	* {{cite journal
	~~\|last=Dutilleul \|first=P~~
	~~\|year=1999~~
	~~\|title=The MLE algorithm for the matrix normal distribution~~
	~~\|journal=[[Journal of Statistical Computation and Simulation]]~~
	~~\|volume=64 \|issue=2 \|pages=105–123~~
	~~\|doi=10.1080/00949659908811970~~
	}}
	* {{Citation
	~~\|last=Arnold \|first=S.F.~~
	~~\|title=The theory of linear models and multivariate analysis~~
	~~\|publisher=[[John Wiley & Sons]]~~
	~~\|place=New York~~
	~~\|year=1981~~
	~~\|isbn=0471050652~~
	}}

	~~{{ProbDistributions\|multivariate}}~~

	~~[[Category:Random matrices]]~~
	~~[[Category:Continuous distributions]]~~
	~~[[Category:Multivariate continuous distributions]]~~
	~~[[Category:Probability distributions]~~]

en>Friend of facts2: /* Types */ Correct a spacing issue

2014-02-04T00:09:42Z

Types: Correct a spacing issue

← Older revision		Revision as of 02:09, 4 February 2014
Line 1:		Line 1:
	~~Particular person who wrote~~ the is ~~called Eusebio~~. ~~South Carolina~~ is ~~your boyfriend~~'~~s birth place~~. The ~~beloved hobby for him and his kids~~ is up to ~~fish~~ and he's ~~really been doing it for~~ a ~~very long time~~. ~~Filing has been his profession~~ for ~~a long time. Go to his website to search out out more~~: ~~http~~://~~prometeu.net~~<br><br>~~Here~~ is ~~my web blog~~ - ~~clash of clans cheats~~ - [~~http~~://~~prometeu~~.~~net click~~ the ~~following webpage~~],		{{Probability distribution
			\| name =Matrix normal
			\| type =density
			\| box_width =195px
			\| pdf_image =
			\| cdf_image =
			\| notation =<math>\mathcal{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math>
			\| parameters =<math>\mathbf{M}</math> [[location parameter\|location]] ([[real number\|real]] <math>n\times p</math> [[matrix (mathematics)\|matrix]])<br/>
			<math>\mathbf{U}</math> [[scale matrix\|scale]] ([[positive-definite matrix\|positive-definite]] [[real number\|real]] <math>n\times n</math> [[matrix (mathematics)\|matrix]])<br/>
			<math>\mathbf{V}</math> [[scale matrix\|scale]] ([[positive-definite matrix\|positive-definite]] [[real number\|real]] <math>p\times p</math> [[matrix (mathematics)\|matrix]])
			\| support =<math>\mathbf{X} \in \mathbb{R}^{n \times p}</math>
			\| pdf =<math>\frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left[ \mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{T} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np/2} \|\mathbf{V}\|^{n/2} \|\mathbf{U}\|^{p/2}}</math>
			\| cdf =
			\| mean =<math>\mathbf{M}</math>
			\| median =
			\| mode =
			\| variance =<math>\mathbf{U}</math> (among-row) and <math>\mathbf{V}</math> (among-column)
			\| skewness =
			\| kurtosis =
			\| entropy =
			\| mgf =
			\| char =
			}}

			In [[statistics]], the '''matrix normal distribution''' is a [[probability distribution]] that is a generalization of the [[multivariate normal distribution]] to matrix-valued random variables.

			== Definition ==
			The [[probability density function]] for the random matrix '''X''' (''n'' × ''p'') that follows the matrix normal distribution <math>\mathcal{MN}_{n,p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math> has the form:

			:<math>
			p(\mathbf{X}\|\mathbf{M}, \mathbf{U}, \mathbf{V}) = \frac{\exp\left( -\frac{1}{2} \, \mathrm{tr}\left[ \mathbf{V}^{-1} (\mathbf{X} - \mathbf{M})^{T} \mathbf{U}^{-1} (\mathbf{X} - \mathbf{M}) \right] \right)}{(2\pi)^{np/2} \|\mathbf{V}\|^{n/2} \|\mathbf{U}\|^{p/2}}
			</math>

			where '''M''' is ''n'' × ''p'', '''U''' is ''n'' × ''n'' and '''V''' is ''p'' × ''p''.

			There are several ways to define the two covariance matrices. One possibility is

			:<math>\mathbf{U} = E[(\mathbf{X} - \mathbf{M})(\mathbf{X} - \mathbf{M})^{T}]</math>

			:<math>\mathbf{V} = E[(\mathbf{X} - \mathbf{M})^{T} (\mathbf{X} - \mathbf{M})] / c</math>

			where <math>c</math> is a constant which depends on '''U''' and ensures appropriate power normalization.

			The matrix normal is related to the [[multivariate normal distribution]] in the following way:

			:<math>\mathbf{X} \sim \mathcal{MN}_{n\times p}(\mathbf{M}, \mathbf{U}, \mathbf{V}),</math>

			if and only if

			:<math>\mathrm{vec}(\mathbf{X}) \sim \mathcal{N}_{np}(\mathrm{vec}(\mathbf{M}), \mathbf{V} \otimes \mathbf{U})</math>

			where <math>\otimes</math> denotes the [[Kronecker product]] and <math>\mathrm{vec}(\mathbf{M})</math> denotes the [[vectorization (mathematics)\|vectorization]] of <math>\mathbf{M}</math>.

			==Example==
			Let's imagine a sample of ''n'' independent ''p''-dimensional random variables identically distributed according to a [[multivariate normal distribution]]:
			:<math>\mathbf{Y}_i \sim \mathcal{N}_p({\boldsymbol \mu}, {\boldsymbol \Sigma}) \text{ with } i \in \{1,\ldots,n\}</math>.
			When defining the ''n'' × ''p'' matrix <math>\mathbf{X}</math> for which the ''i''th row is <math>\mathbf{Y}_i</math>, we obtain:
			:<math>\mathbf{X} \sim \mathcal{MN}_{n \times p}(\mathbf{M}, \mathbf{U}, \mathbf{V})</math>
			where each row of <math>\mathbf{M}</math> is equal to <math>{\boldsymbol \mu}</math>, that is <math>\mathbf{M}=\mathbf{1}_n \times {\boldsymbol \mu}^T</math>, <math>\mathbf{U}</math> is the ''n'' × ''n'' identity matrix, that is the rows are independent, and <math>\mathbf{V} = {\boldsymbol \Sigma}</math>.

			==Relation to other distributions==
			Dawid (1981) provides a discussion of the relation of the matrix-valued normal distribution to other distributions, including the [[Wishart distribution]], [[Inverse Wishart distribution]] and [[matrix t-distribution]], but uses different notation from that employed here.

			== See also ==
			* [[Multivariate normal distribution]].

			==References==
			* {{cite journal
			\|last=Dawid \|first=A.P. \|authorlink=Philip Dawid
			\|year=1981
			\|title=Some matrix-variate distribution theory: Notational considerations and a Bayesian application
			\|journal=[[Biometrika]]
			\|volume=68 \|issue=1 \|pages=265–274
			\|doi=10.1093/biomet/68.1.265 \|mr=614963 \| jstor = 2335827
			}}
			* {{cite journal
			\|last=Dutilleul \|first=P
			\|year=1999
			\|title=The MLE algorithm for the matrix normal distribution
			\|journal=[[Journal of Statistical Computation and Simulation]]
			\|volume=64 \|issue=2 \|pages=105–123
			\|doi=10.1080/00949659908811970
			}}
			* {{Citation
			\|last=Arnold \|first=S.F.
			\|title=The theory of linear models and multivariate analysis
			\|publisher=[[John Wiley & Sons]]
			\|place=New York
			\|year=1981
			\|isbn=0471050652
			}}

			{{ProbDistributions\|multivariate}}

			[[Category:Random matrices]]
			[[Category:Continuous distributions]]
			[[Category:Multivariate continuous distributions]]
			[[Category:Probability distributions]]

18.189.90.127: omega^2 is biased, although less biased than eta^2 (see the Olejnik paper)

2012-08-21T02:02:14Z

omega^2 is biased, although less biased than eta^2 (see the Olejnik paper)

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