Sphericity - Revision history

177.5.157.6 at 22:26, 26 December 2014

2014-12-26T22:26:36Z

← Older revision		Revision as of 00:26, 27 December 2014
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en>DexDor: /* External links */ +Wiktionary, rm non-defining cat

2014-02-09T06:05:58Z

External links: +Wiktionary, rm non-defining cat

← Older revision		Revision as of 08:05, 9 February 2014
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	~~In [[probability theory]]~~, '~~''Le Cam's theorem''', named after [[Lucien le Cam]] (1924 – 2000),~~ is ~~as follows.~~		I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my complete name. To climb is something I truly enjoy doing. My wife and I reside in Kentucky. He works as a bookkeeper.<br><br>Here is my web blog ... online psychic - [http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 sneak a peek at this website],

	~~Suppose:~~

	* ''X''<sub>1</sub>, ..~~., ''X''<sub>''n''</sub> are [[statistical independence\|independent]] [[random variable]]s, each with~~ a ~~[[Bernoulli distribution]] (i.e., equal to either 0 or 1), not necessarily identically distributed~~.

	* Pr(''X''<~~sub~~>~~''i''~~<~~/sub~~> ~~= 1) = ''p''<sub>''i''</sub> for ''i'' = 1, 2, 3, ...~~

	* <math>\lambda_n = p_1 + \cdots + p_n.\,</math>

	* <math>S_n = X_1 + \cdots + X_n.~~\,</math> (i~~.e. ~~<math>S_n</math> follows a [[Poisson binomial distribution]])~~

	~~Then~~

	~~:<math>\sum_{k=0}^\infty \left\| \Pr(S_n=k) - {\lambda_n^k e^{~~-~~\lambda_n} \over k!} \right\| < 2 \sum_{i=1}^n p_i^2. </math>~~

	~~In other words, the sum has approximately a [[Poisson distribution]].~~

	~~By setting ''p''<sub>''i''</sub> = λ<sub>''n''</sub>/''n'', we see that this generalizes the usual [~~[~~Poisson limit theorem]].~~

	~~==References==~~
	* {{cite journal
	~~\|last=Le Cam \|first=L. \|authorlink=Lucien le Cam~~
	~~\|title=An Approximation Theorem for the Poisson Binomial Distribution~~
	~~\|journal=Pacific Journal of Mathematics~~
	~~\|volume=10 \|issue=4 \|pages=1181–1197 \|year=1960~~
	~~\|url=~~http://~~projecteuclid.org/euclid~~.~~pjm~~/~~1103038058 \|accessdate=2009-05-13~~
	~~\|mr=0142174 \| zbl = 0118~~.~~33601~~
	}}
	* {{cite conference
	~~\|last~~=~~Le Cam \|first=L. \|authorlink=Lucien le Cam~~
	~~\|title=On the Distribution of Sums of Independent Random Variables~~
	~~\|booktitle=Bernoulli, Bayes, Laplace: Proceedings of an International Research Seminar~~
	~~\|editor1=[[Jerzy Neyman]] \|editor2=Lucien le Cam~~
	~~\|publisher=Springer-Verlag \|location~~=~~New York~~
	~~\|pages=179~~&~~ndash;202 \|year~~=~~1963~~
	~~\|mr=0199871~~
	}}
	* {{cite jstor\|2325124}}

	~~==External links==~~
	* {{MathWorld\|urlname=LeCamsInequality\|title=Le Cam's Inequality}}

	~~[[Category:Probability theorems]]~~
	~~[[Category:Probabilistic inequalities]]~~
	~~[[Category:Statistical inequalities]]~~
	~~[[Category:Statistical theorems]~~]

en>Mikhail Ryazanov: /* Ellipsoidal objects */ why "defined"?

2013-09-29T03:56:27Z

Ellipsoidal objects: why "defined"?

← Older revision		Revision as of 05:56, 29 September 2013
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	~~Hi there~~, ~~I am Alyson Pomerleau and I think it seems quite great when you say it~~. ~~He functions as~~ a ~~bookkeeper~~. ~~To play lacross is something he would never give up~~. ~~Her family lives in Ohio~~.<br><br>~~my webpage~~ :~~: best psychic~~ ([http://~~breenq~~.~~com~~/~~index~~.~~php?do~~=~~/profile~~-~~1144/info/ visit~~ the ~~following internet page~~])		In [[probability theory]], '''Le Cam's theorem''', named after [[Lucien le Cam]] (1924 – 2000), is as follows.

			Suppose:

			* ''X''<sub>1</sub>, ..., ''X''<sub>''n''</sub> are [[statistical independence\|independent]] [[random variable]]s, each with a [[Bernoulli distribution]] (i.e., equal to either 0 or 1), not necessarily identically distributed.

			* Pr(''X''<sub>''i''</sub> = 1) = ''p''<sub>''i''</sub> for ''i'' = 1, 2, 3, ...

			* <math>\lambda_n = p_1 + \cdots + p_n.\,</math>

			* <math>S_n = X_1 + \cdots + X_n.\,</math> (i.e. <math>S_n</math> follows a [[Poisson binomial distribution]])

			Then

			:<math>\sum_{k=0}^\infty \left\| \Pr(S_n=k) - {\lambda_n^k e^{-\lambda_n} \over k!} \right\| < 2 \sum_{i=1}^n p_i^2. </math>

			In other words, the sum has approximately a [[Poisson distribution]].

			By setting ''p''<sub>''i''</sub> = λ<sub>''n''</sub>/''n'', we see that this generalizes the usual [[Poisson limit theorem]].

			==References==
			* {{cite journal
			\|last=Le Cam \|first=L. \|authorlink=Lucien le Cam
			\|title=An Approximation Theorem for the Poisson Binomial Distribution
			\|journal=Pacific Journal of Mathematics
			\|volume=10 \|issue=4 \|pages=1181–1197 \|year=1960
			\|url=http://projecteuclid.org/euclid.pjm/1103038058 \|accessdate=2009-05-13
			\|mr=0142174 \| zbl = 0118.33601
			}}
			* {{cite conference
			\|last=Le Cam \|first=L. \|authorlink=Lucien le Cam
			\|title=On the Distribution of Sums of Independent Random Variables
			\|booktitle=Bernoulli, Bayes, Laplace: Proceedings of an International Research Seminar
			\|editor1=[[Jerzy Neyman]] \|editor2=Lucien le Cam
			\|publisher=Springer-Verlag \|location=New York
			\|pages=179–202 \|year=1963
			\|mr=0199871
			}}
			* {{cite jstor\|2325124}}

			==External links==
			* {{MathWorld\|urlname=LeCamsInequality\|title=Le Cam's Inequality}}

			[[Category:Probability theorems]]
			[[Category:Probabilistic inequalities]]
			[[Category:Statistical inequalities]]
			[[Category:Statistical theorems]]

en>FrescoBot: Bot: misplaced invisible LTR marks

2012-07-23T05:08:45Z

Bot: misplaced invisible LTR marks

New page

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