Husimi Q representation - Revision history

95.96.43.183 at 18:13, 27 October 2014

2014-10-27T18:13:37Z

← Older revision		Revision as of 20:13, 27 October 2014
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	Branded clothes have always appealed people, whatever could be the age bunch. Don't we all like it as soon as you enter a party and people come to asking what your bought your Gucci shoes, or your Ralph Lauren shirt including? Brands have a certain appeal to them, that's probably the reason why we all like to flaunt the following. Thanks to the increased media attention on the life-style of celebrities, people turn into conscious about the way excellent. After all you wouldn't make sure dead, on last season's shoes.<br><br>At last, the body's harmony along with the movement's stability are very significant. That produce players who can throw the ball into the basket after he can't keep their air jordan shoes balanced. This player's coordination is ~~sufficient. The player can keep his body and his hands stable when he shoots. Players should keep good condition and be very assured. Therefore they can play well~~ in ~~rivalry was announced and win at remaining.<br><br>These shoes have become a household name and Nike caters to every types~~ of shoes - both formal wear as well as casual wear. May different designs and they keep adding day during the day. Nike shoes are worth every penny. These sneakers are also equally durable and lend comfort. Many celebrities endorse these shoes and system another primary reason for their popularity. The footwear are accessible in all elements the world and and are avalable at leading stockists and distributors.<br>~~<br>What~~'s ~~more, the air jordan series consists~~ of ~~air jordan 11 cool greyair Jordan 11 space jamair Jordan 11 whiteAir Jordan xiair Jordan concord, etc~~. ~~Visit our website and search for the fittest site for you~~.<br>~~<br>Other Celebrities fond of Air Jordan shoes are Travis~~ and ~~Disashi within~~ the ~~Gym Class Heroes. Travis is famous for wearing the Air penny 2- black/royal grey. While Disashi likes sporting atmosphere Jordan 8~~ (~~VIII~~) ~~Retro - Aqua's~~.<br><br>Ludacris another celebrity is usually famously seen rocking whilst Air Jordan 3 black/cement. These tend to be simply but several hip hop celebrities who often rocks wearing Jordan brand of trainers. In Hollywood possibilities a dozen others who fancy these brands of sneakers.<br><br>~~If you loved this information in addition to you wish to acquire details relating to~~ [http://~~www.plongeeo~~.com/~~chaussure-air-jordan-pas-cher/ chaussure jordan pas cher~~] ~~i implore you to go to the web-page.~~		Hello! My name is Magdalena. <br>It is a little about myself: I live in Netherlands, my city of Lunteren. <br>It's called often Northern or cultural capital of GE. I've married 3 years ago.<br>I have 2 children - a son (Magdalena) and the daughter (Ned). We all like Tennis.<br><br>Also visit my blog post; [http://tinyurl.com/mgupjtd UGG Boots Outlet]

en>Cuzkatzimhut: /* Definition and properties */

2014-02-07T14:51:41Z

Definition and properties

← Older revision		Revision as of 16:51, 7 February 2014
Line 1:		Line 1:
	~~{{Cleanup\|date=March 2008}}~~		Branded clothes have always appealed people, whatever could be the age bunch. Don't we all like it as soon as you enter a party and people come to asking what your bought your Gucci shoes, or your Ralph Lauren shirt including? Brands have a certain appeal to them, that's probably the reason why we all like to flaunt the following. Thanks to the increased media attention on the life-style of celebrities, people turn into conscious about the way excellent. After all you wouldn't make sure dead, on last season's shoes.<br><br>At last, the body's harmony along with the movement's stability are very significant. That produce players who can throw the ball into the basket after he can't keep their air jordan shoes balanced. This player's coordination is sufficient. The player can keep his body and his hands stable when he shoots. Players should keep good condition and be very assured. Therefore they can play well in rivalry was announced and win at remaining.<br><br>These shoes have become a household name and Nike caters to every types of shoes - both formal wear as well as casual wear. May different designs and they keep adding day during the day. Nike shoes are worth every penny. These sneakers are also equally durable and lend comfort. Many celebrities endorse these shoes and system another primary reason for their popularity. The footwear are accessible in all elements the world and and are avalable at leading stockists and distributors.<br><br>What's more, the air jordan series consists of air jordan 11 cool greyair Jordan 11 space jamair Jordan 11 whiteAir Jordan xiair Jordan concord, etc. Visit our website and search for the fittest site for you.<br><br>Other Celebrities fond of Air Jordan shoes are Travis and Disashi within the Gym Class Heroes. Travis is famous for wearing the Air penny 2- black/royal grey. While Disashi likes sporting atmosphere Jordan 8 (VIII) Retro - Aqua's.<br><br>Ludacris another celebrity is usually famously seen rocking whilst Air Jordan 3 black/cement. These tend to be simply but several hip hop celebrities who often rocks wearing Jordan brand of trainers. In Hollywood possibilities a dozen others who fancy these brands of sneakers.<br><br>If you loved this information in addition to you wish to acquire details relating to [http://www.plongeeo.com/chaussure-air-jordan-pas-cher/ chaussure jordan pas cher] i implore you to go to the web-page.

	~~In [[statistics]]~~, the '~~''multinomial test''' is the test of the [[null hypothesis]] that the parameters of~~ a ~~[[multinomial distribution]] equal specified values. It is used for categorical data; see Read~~ and ~~Cressie.<ref>Read~~, ~~T. R. C. and Cressie~~, ~~N. A. C. (1988).~~ '~~'Goodness-of-fit statistics for discrete multivariate data~~.~~'' New York: Springer~~-~~Verlag. ISBN 0-387-96682-X.</ref>~~

	~~We begin with a sample~~ of ~~<math>N</math> items each of which has been observed to fall~~ into ~~one of <math>k</math> categories~~. ~~We can define <math>\mathbf{x} = (x_1~~, ~~x_2, \dots, x_k)</math> as the observed numbers of items in each cell~~. ~~Hence~~ <~~math~~>~~\textstyle \sum_{i=1}^k x_{i} = N~~<~~/math~~>.

	~~Next~~, ~~we define a vector of parameters <math>H_0: \mathbf{\pi} = (\pi_{1}, \pi_{2}, \dots, \pi_{k})</math>, where :<math>\textstyle \sum_{i=1}^k \pi_{i} = 1</math>. These are~~ the ~~parameter values under~~ the ~~[[null hypothesis]]~~.

	~~The exact probability of~~ the ~~observed configuration <math>\mathbf{x} </math> under~~ the ~~null hypothesis~~ is ~~given by~~

	~~:<math>\Pr(\mathbf{x)_0} = N! \prod_{i=1}^k \frac{\pi_{i}^{x_i}}{x_i!}~~.~~</math>~~

	The ~~significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true~~. ~~Using an [[exact test]], this is calculated as~~

	:<~~math~~>~~\Pr(\mathbf{sig})=\sum_{y: Pr(\mathbf{y}) \le Pr(\mathbf{x)_0}} \Pr(\mathbf{y})~~<~~/math~~>

	~~where the sum ranges over all outcomes~~ as ~~likely~~ as~~, or less likely than, that observed~~. ~~In practice this becomes computationally onerous as <math>k</math>~~ and ~~<math>N</math> increase so it is probably only~~ worth ~~using exact tests for small samples~~. ~~For larger samples, asymptotic approximations~~ are ~~accurate enough~~ and ~~easier to calculate~~.

	~~One of~~ these approximations is the [[Likelihood-ratio test\|likelihood ratio]]. We set up an [[alternative hypothesis]] under which each value <math>\pi_{i}</math> is replaced by its maximum likelihood estimate <math>p_{i}=x_{i}/N</math>. The ~~exact probability of~~ the ~~observed configuration <math>\mathbf{x} </math> under the alternative hypothesis is given by~~

	~~: <math>\Pr(\mathbf{x)_A} = N! \prod_{i=1}^k \frac{p_{i}^{x_i}}{x_i!}~~.<~~/math~~>

	~~The natural logarithm of the ratio between these two probabilities multiplied by~~ <~~math~~>~~-2</math> is then the statistic for the [[likelihood ratio test]]~~

	~~: <math>-2\ln(LR) = \textstyle -2\sum_{i=1}^k x_{i}\ln(\pi_{i}/p_{i}) .</math>~~

	~~If the null hypothesis is true, then as <math>N</math> increases~~, the ~~distribution~~ of ~~<math>-2\ln(LR) </math> converges to that of [[Chi-squared distribution\|chi-squared]] with <math>k-1</math> degrees of freedom~~. ~~However it has long been known (e.g. Lawley 1956) that~~ for ~~finite sample sizes,~~ the ~~moments of~~ <~~math~~>~~-2\ln(LR)~~ <~~/math~~> are ~~greater than those of chi-squared, thus inflating~~ the ~~probability of [[Type I and type II errors\|type I errors]] (false positives)~~. ~~The difference between~~ the ~~moments of chi~~-~~squared and those of the test statistic are a function of <math>N^{-1}<~~/~~math>~~. ~~Williams~~ (~~1976~~) ~~showed that the first moment can be matched as far as <math>N^{~~-2}<~~/math~~> ~~if the test statistic is divided by a factor given by~~

	: <~~math~~>~~q_1 = 1+\frac{\sum_{i=1}^k \pi_{i}^{-1}-1}{6N(k-1)}. </math>~~

	~~In the special case where the null hypothesis~~ is ~~that all the values <math>\pi_{i}<~~/~~math> are equal to <math>1/k</math> (i~~.~~e. it stipulates a uniform distribution), this simplifies~~ to

	~~: <math>q_1 = 1+\frac{k+1}{6N}~~. ~~</math>~~

	~~Subsequently, Smith et al. (1981) derived~~ a ~~dividing factor which matches the first moment as far as <math>N^{-3}</math>~~. ~~For the case of equal values of~~ <~~math~~>~~\pi_{i}~~<~~/math~~>, this ~~factor is~~

	~~: <math>q_2 = 1+\frac{k+1}{6N}+\frac{k^2}{6N^2}. </math>~~

	~~The null hypothesis can also be tested by using~~ [~~[Pearson's chi-squared test]]~~

	:~~<math> \chi^2 = \sum_{i=1}^{k} {(x_i - E_i)^2 \over E_i}<~~/~~math>~~

	~~where <math>E_i=N\pi_i<~~/~~math> is the expected number of cases in category <math>i<~~/~~math> under the null hypothesis. This statistic also converges to a chi~~-~~squared distribution with <math>k~~-~~1</math> degrees of freedom when the null hypothesis is true but does so from below, as it were, rather than from above as <math>~~-~~2\ln(LR) <~~/~~math> does, so may be preferable~~ to the ~~uncorrected version of <math>~~-~~2\ln(LR) </math> for small samples.~~

	~~== References ==~~
	~~<references/>~~
	*{{cite journal \| author=Lawley, D. N. \| title=A General Method of Approximating to the Distribution of Likelihood Ratio Criteria \| journal=Biometrika \| year=1956 \| volume=43 \| pages=295–303}}
	*{{cite journal \| author=Smith, P. J., Rae, D. S., Manderscheid, R. W. and Silbergeld, S.\| title=Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit \| journal=Journal of the American Statistical Association \| year=1981 \| volume=76 \| pages=737–740 \| doi=10.2307/2287541 \| issue=375 \| publisher=American Statistical Association \| jstor=2287541}}
	*{{cite journal \| author=Williams, D. A. \| title=Improved Likelihood Ratio Tests for Complete Contingency Tables \| journal=Biometrika \| year=1976 \| volume=63 \| pages=33–37 \| doi=10.1093/biomet/63.~~1.33}}~~

	~~[[Category:Categorical data]]~~
	~~[[Category:Statistical tests]]~~
	~~[[Category:Non-parametric statistics]]~~

en>Cuzkatzimhut at 11:59, 20 December 2013

2013-12-20T11:59:49Z

← Older revision		Revision as of 13:59, 20 December 2013
Line 1:		Line 1:
			{{Cleanup\|date=March 2008}}

			In [[statistics]], the '''multinomial test''' is the test of the [[null hypothesis]] that the parameters of a [[multinomial distribution]] equal specified values. It is used for categorical data; see Read and Cressie.<ref>Read, T. R. C. and Cressie, N. A. C. (1988). ''Goodness-of-fit statistics for discrete multivariate data.'' New York: Springer-Verlag. ISBN 0-387-96682-X.</ref>

	~~e - Shop Word - Press is~~ a ~~excellent cart for your on the web shopping organization. This one is~~ one of the ~~most beneficial features~~ of ~~Word - Press as this feature allows users to~~ define the ~~user roles~~. ~~Step-4 Testing~~: It is the ~~foremost important~~ of ~~your Plugin development process. Out~~ of the ~~various designs~~ of ~~photography identified these days~~, ~~sports photography~~ is ~~preferred most~~, ~~probably for~~ the ~~enjoyment and enjoyment associated with it~~. In ~~the most current edition you can customize your retailer layout~~ and ~~display hues and fonts similar to your site or blog.~~ <br><br>~~The Internet~~ is ~~a vast open market where businesses and consumers congregate. Wordpress have every reason with it which promote wordpress development~~. ~~It sorts the results of a search according to category~~, ~~tags~~ and ~~comments~~. ~~So, if you are looking for some option to build a giant e~~-~~commerce website, then e-shopping preferable CMS tools will be helpful for you~~. ~~Aided~~ by the ~~completely foolproof j - Query color selector, you're able to change~~ the ~~colors~~ of ~~factors of your theme a~~ the ~~click on the screen, with very little previous web site design experience.~~ <br><br>~~ve labored so hard to publish and put up on their website. Now if we talk about them one by one~~ then -~~wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire~~ the ~~SEO friendly blog application integrated with your site design~~ as ~~well as separate blog administration panel for starting up your own business blog~~,~~which demands a experienced wordpress designer. After age 35, 18%~~ of ~~pregnancies will end in miscarriage. Storing write~~-~~ups in advance would have~~ to ~~be neccessary~~ with ~~the auto blogs~~. ~~Have you heard about niche marketing and advertising~~. <br><br>~~It has become a more prevalent cause~~ of ~~infertility and~~ the ~~fertility clinic are having more~~ and ~~more couples with infertility problems~~. ~~And, make no mistake,India's Fertility Clinics~~ and ~~IVF specialists~~ are ~~amongst the best in the world,and have been for some time. Next you'll go by way~~ of ~~to your simple Word~~ - ~~Press site~~. ~~A whole lot worse, your site will likely~~ be ~~useless~~ as ~~well~~ as ~~your merchandise won't sell~~ if ~~no one has~~ the ~~endurance to wait for~~ the ~~web pages~~ to ~~load~~. ~~Word - Press offers constant updated services and products~~, ~~that too~~, ~~absolutely free of cost~~. <br><br>In case ~~you loved~~ this ~~short article and you would like to receive details with regards to~~ [~~http~~://~~ll.my~~/~~wordpressdropboxbackup288861 wordpress backup plugin] generously visit our web site~~. ~~Someone with a basic knowledge of setting up a website should be able~~ to ~~complete the process in~~ a ~~couple~~ of ~~minutes however even basic users should find they are able to complete~~ the ~~installation in around 20 minutes by following the step by step guide online. In fact portfolio Word - Press themes~~ is ~~a smooth and attractive~~ but ~~considerably flawed Word~~ - ~~Press theme in creating simpler~~ to the ~~photographers or designers to develop a specific internet site showcasing their most current perform since it appear modern~~-~~day and has fantastic typography and large photographs which would develop an attractive wanting portfolio internet site~~. ~~Must being~~, ~~it's beneficial because I don't know about you~~, ~~but loading an old website on a mobile~~, ~~having to scroll down~~, up, and ~~sideways' I find links being clicked and bounced around like I'm on a freaking trampoline~~. ~~Web developers~~ and ~~newbies alike will have~~ the ~~ability to extend your web site and fit other incredible functions with out having to spend more~~. ~~However~~, ~~if you're just starting out your blog site or business site, you can still search~~ for ~~an ideal theme for it without breaking your bank account~~.		We begin with a sample of <math>N</math> items each of which has been observed to fall into one of <math>k</math> categories. We can define <math>\mathbf{x} = (x_1, x_2, \dots, x_k)</math> as the observed numbers of items in each cell. Hence <math>\textstyle \sum_{i=1}^k x_{i} = N</math>.

			Next, we define a vector of parameters <math>H_0: \mathbf{\pi} = (\pi_{1}, \pi_{2}, \dots, \pi_{k})</math>, where :<math>\textstyle \sum_{i=1}^k \pi_{i} = 1</math>. These are the parameter values under the [[null hypothesis]].

			The exact probability of the observed configuration <math>\mathbf{x} </math> under the null hypothesis is given by

			:<math>\Pr(\mathbf{x)_0} = N! \prod_{i=1}^k \frac{\pi_{i}^{x_i}}{x_i!}.</math>

			The significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true. Using an [[exact test]], this is calculated as

			:<math>\Pr(\mathbf{sig})=\sum_{y: Pr(\mathbf{y}) \le Pr(\mathbf{x)_0}} \Pr(\mathbf{y})</math>

			where the sum ranges over all outcomes as likely as, or less likely than, that observed. In practice this becomes computationally onerous as <math>k</math> and <math>N</math> increase so it is probably only worth using exact tests for small samples. For larger samples, asymptotic approximations are accurate enough and easier to calculate.

			One of these approximations is the [[Likelihood-ratio test\|likelihood ratio]]. We set up an [[alternative hypothesis]] under which each value <math>\pi_{i}</math> is replaced by its maximum likelihood estimate <math>p_{i}=x_{i}/N</math>. The exact probability of the observed configuration <math>\mathbf{x} </math> under the alternative hypothesis is given by

			: <math>\Pr(\mathbf{x)_A} = N! \prod_{i=1}^k \frac{p_{i}^{x_i}}{x_i!}.</math>

			The natural logarithm of the ratio between these two probabilities multiplied by <math>-2</math> is then the statistic for the [[likelihood ratio test]]

			: <math>-2\ln(LR) = \textstyle -2\sum_{i=1}^k x_{i}\ln(\pi_{i}/p_{i}) .</math>

			If the null hypothesis is true, then as <math>N</math> increases, the distribution of <math>-2\ln(LR) </math> converges to that of [[Chi-squared distribution\|chi-squared]] with <math>k-1</math> degrees of freedom. However it has long been known (e.g. Lawley 1956) that for finite sample sizes, the moments of <math>-2\ln(LR) </math> are greater than those of chi-squared, thus inflating the probability of [[Type I and type II errors\|type I errors]] (false positives). The difference between the moments of chi-squared and those of the test statistic are a function of <math>N^{-1}</math>. Williams (1976) showed that the first moment can be matched as far as <math>N^{-2}</math> if the test statistic is divided by a factor given by

			: <math>q_1 = 1+\frac{\sum_{i=1}^k \pi_{i}^{-1}-1}{6N(k-1)}. </math>

			In the special case where the null hypothesis is that all the values <math>\pi_{i}</math> are equal to <math>1/k</math> (i.e. it stipulates a uniform distribution), this simplifies to

			: <math>q_1 = 1+\frac{k+1}{6N}. </math>

			Subsequently, Smith et al. (1981) derived a dividing factor which matches the first moment as far as <math>N^{-3}</math>. For the case of equal values of <math>\pi_{i}</math>, this factor is

			: <math>q_2 = 1+\frac{k+1}{6N}+\frac{k^2}{6N^2}. </math>

			The null hypothesis can also be tested by using [[Pearson's chi-squared test]]

			:<math> \chi^2 = \sum_{i=1}^{k} {(x_i - E_i)^2 \over E_i}</math>

			where <math>E_i=N\pi_i</math> is the expected number of cases in category <math>i</math> under the null hypothesis. This statistic also converges to a chi-squared distribution with <math>k-1</math> degrees of freedom when the null hypothesis is true but does so from below, as it were, rather than from above as <math>-2\ln(LR) </math> does, so may be preferable to the uncorrected version of <math>-2\ln(LR) </math> for small samples.

			== References ==
			<references/>
			*{{cite journal \| author=Lawley, D. N. \| title=A General Method of Approximating to the Distribution of Likelihood Ratio Criteria \| journal=Biometrika \| year=1956 \| volume=43 \| pages=295–303}}
			*{{cite journal \| author=Smith, P. J., Rae, D. S., Manderscheid, R. W. and Silbergeld, S.\| title=Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit \| journal=Journal of the American Statistical Association \| year=1981 \| volume=76 \| pages=737–740 \| doi=10.2307/2287541 \| issue=375 \| publisher=American Statistical Association \| jstor=2287541}}
			*{{cite journal \| author=Williams, D. A. \| title=Improved Likelihood Ratio Tests for Complete Contingency Tables \| journal=Biometrika \| year=1976 \| volume=63 \| pages=33–37 \| doi=10.1093/biomet/63.1.33}}

			[[Category:Categorical data]]
			[[Category:Statistical tests]]
			[[Category:Non-parametric statistics]]

en>Teply: /* Definition and properties */

2012-08-02T09:03:07Z

Definition and properties

New page

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