Derived demand - Revision history

122.179.179.180 at 21:00, 28 November 2014

2014-11-28T21:00:43Z

← Older revision		Revision as of 23:00, 28 November 2014
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	~~{{Dablink\|This article is about the method of moments in [[probability theory]]. See [[method of moments]] for other techniques bearing the same name.}}~~		Hello, my title is Andrew and my spouse doesn't like it at all. I am an invoicing officer and I'll be promoted quickly. What me and my family members love is bungee leaping but I've been taking on new things recently. Alaska is where I've usually been living.<br><br>Also visit my page - free psychic readings ([http://www.publicpledge.com/blogs/post/7034 click through the next document])

	In [[probability theory]], the '''method of moments''' is a way of proving [[convergence in distribution]] by proving convergence of a sequence of [[moment (mathematics)\|moment]] sequences.<ref>{{cite book\|last=Prokhorov\|first=A.V.\|chapter=Moments, ~~method of (in probability theory)\|~~title~~=Encyclopaedia of Mathematics (online)\|isbn=1-4020-0609-8\|url=http://eom.springer.de/m/m064610.htm\|mr=1375697\|editor=M. Hazewinkel}}</ref> Suppose ''X''~~ is ~~a [[random variable]]~~ and ~~that~~ all ~~of the moments~~

	~~:<math>\operatorname{E}(X^k)\,</math>~~

	~~exist~~. ~~Further suppose the [[probability distribution]] of~~ ''~~X'' is completely determined by its moments, i~~.~~e., there~~ is ~~no other probability distribution with the same sequence of moments~~
	~~(cf~~. ~~the [[problem of moments]]). If~~

	:<~~math~~>~~\lim_{n\to\infty}\operatorname{E}~~(~~X_n^k) = \operatorname{E}(X^k)\,<~~/~~math>~~

	~~for all values of ''k'', then the sequence {''X''<sub>''n''<~~/~~sub>} converges to ''X'' in distribution.~~

	The method of moments was introduced by [[Pafnuty Chebyshev]] for proving the [[central limit theorem]]; Chebyshev cited earlier contributions by [[Irénée-Jules Bienaymé]].<ref>{{cite book\|mr=2743162\|last=Fischer\|first=H.~~\|title=A history of the central limit theorem~~. From classical to modern probability theory.\|series= Sources and Studies in the History of Mathematics and Physical Sciences\|publisher=Springer\|location=New York\|year=2011\|isbn=978-0-387-87856-0\|chapter=4. Chebyshev's and Markov's Contributions.}}</~~ref> More recently, it has been applied by [[Eugene Wigner]] to prove [[Wigner's semicircle law]], and has since found numerous applications in~~ the ~~[[random matrix theory\|theory of random matrices~~]].<ref>{{cite book\|last=Anderson\|first=G.W.\|last2=Guionnet\|first2=A.\|last3=Zeitouni\|first3=O.\|title=An introduction to random matrices.\|year=2010\|publisher=Cambridge University Press\|location=Cambridge\|isbn=978-0-521-19452-5\|chapter=2.1}}</ref>

	~~==Notes==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Method Of Moments (Probability Theory~~)}}
	~~[[Category:Probability theory]]~~

143.215.24.116: Removed holiday flights as example of derived demand. The good being consumed is the tourist destination, not likely the flight thereto.

2014-02-03T14:10:59Z

Removed holiday flights as example of derived demand. The good being consumed is the tourist destination, not likely the flight thereto.

← Older revision		Revision as of 16:10, 3 February 2014
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	~~She~~ is ~~recognized by~~ the name of ~~Myrtle Shryock~~. It'~~s not~~ a ~~typical factor but what she likes performing~~ is ~~base jumping and now she~~ is ~~attempting~~ to ~~earn cash with it~~. ~~My working day job is a librarian~~. ~~Minnesota is where he~~'s been ~~residing for many years~~.<br><br>~~Here is my weblog :~~: [~~http~~:~~//premium.asslikethat.com/user/CSalerno at home std testing~~]		{{Dablink\|This article is about the method of moments in [[probability theory]]. See [[method of moments]] for other techniques bearing the same name.}}

			In [[probability theory]], the '''method of moments''' is a way of proving [[convergence in distribution]] by proving convergence of a sequence of [[moment (mathematics)\|moment]] sequences.<ref>{{cite book\|last=Prokhorov\|first=A.V.\|chapter=Moments, method of (in probability theory)\|title=Encyclopaedia of Mathematics (online)\|isbn=1-4020-0609-8\|url=http://eom.springer.de/m/m064610.htm\|mr=1375697\|editor=M. Hazewinkel}}</ref> Suppose ''X'' is a [[random variable]] and that all of the moments

			:<math>\operatorname{E}(X^k)\,</math>

			exist. Further suppose the [[probability distribution]] of ''X'' is completely determined by its moments, i.e., there is no other probability distribution with the same sequence of moments
			(cf. the [[problem of moments]]). If

			:<math>\lim_{n\to\infty}\operatorname{E}(X_n^k) = \operatorname{E}(X^k)\,</math>

			for all values of ''k'', then the sequence {''X''<sub>''n''</sub>} converges to ''X'' in distribution.

			The method of moments was introduced by [[Pafnuty Chebyshev]] for proving the [[central limit theorem]]; Chebyshev cited earlier contributions by [[Irénée-Jules Bienaymé]].<ref>{{cite book\|mr=2743162\|last=Fischer\|first=H.\|title=A history of the central limit theorem. From classical to modern probability theory.\|series= Sources and Studies in the History of Mathematics and Physical Sciences\|publisher=Springer\|location=New York\|year=2011\|isbn=978-0-387-87856-0\|chapter=4. Chebyshev's and Markov's Contributions.}}</ref> More recently, it has been applied by [[Eugene Wigner]] to prove [[Wigner's semicircle law]], and has since found numerous applications in the [[random matrix theory\|theory of random matrices]].<ref>{{cite book\|last=Anderson\|first=G.W.\|last2=Guionnet\|first2=A.\|last3=Zeitouni\|first3=O.\|title=An introduction to random matrices.\|year=2010\|publisher=Cambridge University Press\|location=Cambridge\|isbn=978-0-521-19452-5\|chapter=2.1}}</ref>

			==Notes==
			{{Reflist}}

			{{DEFAULTSORT:Method Of Moments (Probability Theory)}}
			[[Category:Probability theory]]

en>Cretog8: Undid revision 500769631 by 121.217.235.112 (talk)

2012-07-05T17:03:14Z

Undid revision 500769631 by 121.217.235.112 (talk)

New page

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