Lagged Fibonacci generator - Revision history

en>Xavier Combelle: revert turkish

2014-07-19T13:58:05Z

revert turkish

← Older revision		Revision as of 15:58, 19 July 2014
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	<li>[http://www.jamiatou.com/spip.php?article21 http://www.jamiatou.com/spip.php?article21]</li>		<li>[http://www.jamiatou.com/spip.php?article21 http://www.jamiatou.com/spip.php?article21]</li>

			</ul>

			== Polo Lacoste Discount 42 millions d'actions de Celltrion ==

			Rupert Murdoch Mesure 1: Know Your Business Action Point 2: ne [http://www.weiermannsystems.com/mitarbeiter/session.asp?polo=116-Polo-Lacoste-Discount Polo Lacoste Discount] manquez pas d'action Point 3: Construire une équipe True Story En Janvier 2012, au large des côtes de Tobago Cays, cinq petites îles inhabitées dans les Grenadines, il y avait tripotée de milliardaires yachts ancrés . Il est David Geffen sur Rising Sun, le plus grand yacht du monde. <br><br>Cela devrait vous donner quelques bonnes idées pour votre site Web. Il sait vraiment ce qu'il fait quand il s'agit de faire de l'argent en ligne et il est la vraie affaire. 19 juin 2013 la technologie de GigaPan est utilisé pour afficher les images prises par la sonde [http://www.tipi-romoos.ch/gefuehrte-touren/header.asp?newbalance=42-Basket-New-Balance-Femme-U420 Basket New Balance Femme U420] Mars rover Curiosity, une mission de la NASA enquête passées et présentes des environnements dans le cratère Gale sur Mars. Géré par le Jet Propulsion Laboratory de la NASA (JPL) à Pasadena, en Californie, le rover a atterri en Août 2012 et est la dernière mission d'explorer la planète rouge. <br><br>Très peu de gens savent beaucoup sur cela et beaucoup de gens (comme moi) savent très peu de choses sur elle. Aucune information ne doit être soumise à ce site par les utilisateurs de moins de 13 ans, et les utilisateurs de moins de 13 ans ne sont pas autorisés à s'inscrire à des bulletins, des clubs ou des activités. <br><br>S'il domaine difficile à pénétrer chiffres concrets sont rares, nous savons pertinemment que les sites pornos sont quelques-unes des pièces les plus fréquentées de l'Internet. Selon Google DoubleClick Ad Planner, qui permet de suivre les utilisateurs du Web avec un cookie, des dizaines de destinations adultes [http://www.audiosam.ch/subgallery/inc/session.asp?nikefree=95-Nike-Free-4.0 Nike Free 4.0] peuplent les 500 meilleurs sites Web. <br><br>Évitez la tentation de porter des talons hauts. Optez pour des sandales strapon confortables appartements à la place. Il a également dirigé la représentation de Skadden Celltrion CGC Co., Ltd Et Celltrion Holdings Co., Ltd Dans la vente de 4,42 millions d'actions de Celltrion, Inc. Il ya très peu de comparaisons à Dalyan quand il s'agit de choisir des destinations de vacances. <br><br>Ils ont été libérés à la fois par l'émancipation volontaire des industriels dans le Nord et les propriétaires altruistes dans le Sud, et par l'échappement d'esclaves dans le Sud et la dévastation économique de l'après-guerre. Si vous pensez que la Proclamation d'émancipation effectivement libéré tout le monde, je vous suggère de regarder un peu plus profondément dans l'histoire ... <br><br>Rapport; âge mûr cougar salope coq noir cul baise et sperme sur Hot Tube il ya 2 mois 05:18. Dans un geste étrange, Josh et Jenna ajoutés [http://www.weiermannsystems.com/mitarbeiter/session.asp?polo=79-Fred-Perry-Lausanne Fred Perry Lausanne] congélateurs par le sol dans leur armoire à linge. Comme nous le savons tous, l'éclairage de la voiture est la partie importante des accessoires automobiles. 3.<ul>

			<li>[http://bbs.sfwenhui.org/forum.php?mod=viewthread&tid=292062 http://bbs.sfwenhui.org/forum.php?mod=viewthread&tid=292062]</li>

			<li>[http://enseignement-lsf.com/spip.php?article369#forum17905236 http://enseignement-lsf.com/spip.php?article369#forum17905236]</li>

			<li>[http://www.ovnprod.com/spip.php?article24/ http://www.ovnprod.com/spip.php?article24/]</li>

			<li>[http://mycoralfarm.com/activity/p/326402/ http://mycoralfarm.com/activity/p/326402/]</li>

			<li>[http://www.shaffaf.net/spip.php?article929&lang=ar&id_forum=27372/ http://www.shaffaf.net/spip.php?article929&lang=ar&id_forum=27372/]</li>

	</ul>		</ul>

en>BG19bot: /* Problems with LFGs */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

2014-02-07T09:03:58Z

Problems with LFGs: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

Show changes

79.41.201.117: /* Note that multiplicative lfg have different initialization requirements wrt additive lfg; TODO mlfg only produce odd numbers */

2013-10-30T21:28:35Z

Note that multiplicative lfg have different initialization requirements wrt additive lfg; TODO mlfg only produce odd numbers

← Older revision		Revision as of 23:28, 30 October 2013
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	~~Hello! My~~ name is ~~Richie~~. <br>It is a little ~~about myself~~: ~~I live~~ in ~~Netherlands~~, ~~my city~~ of ~~Landsmeer~~. <br>~~It's called often Northern or cultural capital of NH~~. ~~I've married 2 years ago~~.<br>~~I have 2 children~~ - a ~~son~~ (~~Tami~~) and the ~~daughter~~ (~~Jacob~~). We ~~all like Australian Football League~~.<br><br>~~Feel free to visit my weblog~~ ... [http://~~contaminate~~.co/~~?attachment_id~~=~~74 fifa coin Generator~~]		'''Inverse transform sampling''' (also known as '''inversion sampling''', the '''inverse probability integral transform''', the '''inverse transformation method''', '''[[Nikolai Smirnov (mathematician)\|Smirnov]] transform''', '''golden rule''',<ref name=aalto>Aalto University, N. Hyvönen, Computational methods in inverse problems. Twelfth lecture https://noppa.tkk.fi/noppa/kurssi/mat-1.3626/luennot/Mat-1_3626_lecture12.pdf</ref> etc.) is a basic method for [[pseudo-random number sampling]], i.e. for generating sample numbers at [[random]] from any [[probability distribution]] given its [[cumulative distribution function]] (cdf).

			The basic idea is to uniformly sample a number <math>u</math> between 0 and 1, interpreted as a probability, and then return the largest number <math>x</math> from the domain of the distribution <math>p(X)</math> such that <math>p(-\infty < X < x) \le u</math>. For example, imagine that <math>p(X)</math> is the standard [[normal distribution]] (i.e. with [[mean]] 0, [[standard deviation]] 1). Then if we choose <math>u = 0.5</math>, we would return 0, because 50% of the probability of a normal distribution occurs in the region where <math>X \le 0</math>. Similarly, if we choose <math>u = 0.975</math>, we would return 1.95996...; if we choose <math>u = 0.995</math>, we would return 2.5758...; if we choose <math>u = 0.999999</math>, we would return 4.891638...; etc. Essentially, we are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs to the left of that number. Intuitively, we are unlikely to choose a number in the tails because there is very little area in them: We'd have to pick a number very close to 0 or 1.

			Computationally, this method involves computing the [[quantile function]] of the distribution — in other words, computing the [[cumulative distribution function]] (CDF) of the distribution (which maps a number in the domain to a probability between 0 and 1) and then inverting that function. This is the source of the term "inverse" or "inversion" in most of the names for this method. Note that for a [[discrete distribution]], computing the CDF is not in general too difficult: We simply add up the individual probabilities for the various points of the distribution. For a [[continuous distribution]], however, we need to integrate the [[probability density function]] (PDF) of the distribution, which is impossible to do analytically for most distributions (including the [[normal distribution]]). As a result, this method may be computationally inefficient for many distributions and other methods are preferred; however, it is a useful method for building more generally applicable samplers such as those based on [[rejection sampling]].

			For the [[normal distribution]], the lack of an analytical expression for the corresponding quantile function means that other methods (e.g. the [[Box–Muller transform]]) may be preferred computationally. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on:<ref>{{cite book \|author=Luc Devroye \|url=http://www.eirene.de/Devroye.pdf \|title=Non-Uniform Random Variate Generation \|publisher=Springer-Verlag \|place=New York \|year=1986}}</ref> see, for example, the [[ziggurat algorithm]] and [[rejection sampling]]. On the other hand, it is possible to approximate the quantile function of the normal distribution extremely accurately using moderate-degree polynomials, and in fact the method of doing this is fast enough that inversion sampling is now the default method for sampling from a normal distribution in the statistical package [[R (programming language)\|R]].

			==Definition==

			The [[probability integral transform]] states that if <math>X</math> is a [[continuous random variable]] with [[cumulative distribution function]] <math>F_X</math>, then the random variable <math>Y=F_X(X)</math> has a [[uniform distribution (continuous)\|uniform distribution]] on [0, 1]. The inverse probability integral transform is just the inverse of this: specifically, if <math>Y</math> has a uniform distribution on [0, 1] and if <math>X</math> has a cumulative distribution <math>F_X</math>, then the cumulative distribution function of the random variable <math>F_X^{-1}(Y)</math> is <math>F_X</math> .

			==The method==

			The problem that the inverse transform sampling method solves is as follows:

			*Let ''X'' be a [[random variable]] whose distribution can be described by the [[cumulative distribution function]] ''F''.
			*We want to generate values of ''X'' which are distributed according to this distribution.

			The inverse transform sampling method works as follows:
			#[[pseudorandom number generator\|Generate a random number]] ''u'' from the standard uniform distribution in the interval [0,1].
			#Compute the value ''x'' such that ''F''(''x'') = ''u''.
			#Take ''x'' to be the random number drawn from the distribution described by ''F''.

			Expressed differently, given a continuous uniform variable ''U'' in [0, 1] and an [[Inverse function\|invertible]] cumulative distribution function ''F'', the random variable ''X'' = ''F''<sup> −1</sup>(''U'') has distribution ''F'' (or, ''X'' is distributed ''F'').

			A treatment of such inverse functions as objects satisfying differential equations can be given.<ref>Steinbrecher, G., Shaw, W.T. (2008). Quantile mechanics. ''European Journal of Applied Mathematics'' 19 (2): 87–112.</ref> Some such differential equations admit explicit power series solutions, despite their non-linearity.

			==Proof of correctness==
			Let ''F'' be a continuous [[cumulative distribution function]], and let ''F''<sup>−1</sup> be its inverse function (using the [[infimum]] because CDFs are weakly monotonic and [[Càdlàg\|right-continuous]]):<ref>{{cite book \|author=Luc Devroye \|title=Non-Uniform Random Variate Generation \|publisher=Springer-Verlag \|place=New York \|year=1986 \|chapter=Section 2.2. Inversion by numerical solution of ''F''(''X'') = ''U'' \|url=http://luc.devroye.org/chapter_two.pdf}}</ref>

			:<math>F^{-1}(u) = \inf\;\{x \mid F(x)\geq u, 0<u<1\}.</math>

			''Claim:'' If ''U'' is a [[uniform distribution (continuous)\|uniform]] random variable on (0, 1) then <math>F^{-1}(U)</math> follows the distribution ''F''.

			''Proof:''

			:<math>
			\begin{align}
			& \Pr(F^{-1}(U) \leq x) \\
			& {} = \Pr(U \leq F(x)) \quad &\text{(applying }F,\text{ which is monotonic, to both sides)} \\
			& {} = F(x)\quad &\text{(because }\Pr(U \leq y) = y,\text{ since }U\text{ is uniform on the unit interval)}.
			\end{align}
			</math>

			== See also ==
			* [[Probability integral transform]]
			* [[Copula (statistics)\|Copula]], defined by means of probability integral transform.
			* [[Quantile function]], for the explicit construction of inverse CDFs.
			* [[Cumulative distribution function#Inverse\|Inverse distribution function]] for a precise mathematical definition for distributions with discrete components.

			==References==

			<references/>

			== External links ==

			{{DEFAULTSORT:Inverse Transform Sampling}}
			[[Category:Monte Carlo methods]]
			[[Category:Non-uniform random numbers]]

75.167.159.227: /* Usage */

2012-08-27T01:42:04Z

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Hello! My name is Richie. It is a little about myself: I live in Netherlands, my city of Landsmeer. It's called often Northern or cultural capital of NH. I've married 2 years ago. I have 2 children - a son (Tami) and the daughter (Jacob). We all like Australian Football League. Feel free to visit my weblog ... [http://contaminate.co/?attachment_id=74 fifa coin Generator]