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| {{Probability distribution |
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| name =Skew Normal|
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| type =density|
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| pdf_image =[[Image:Skew normal densities.svg|325px|Probability density plots of skew normal distributions]]|
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| cdf_image =[[Image:Skew normal cdfs.svg|325px|Cumulative distribution function plots of skew normal distributions]]|
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| parameters =<math>\xi \,</math> [[location parameter|location]] ([[real number|real]])<br/><math>\omega \,</math> [[scale parameter|scale]] (positive, [[real number|real]])<br/><math>\alpha \,</math> [[shape parameter|shape]] ([[real number|real]])|
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| support =<math>x \in (-\infty; +\infty)\!</math>|
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| pdf = <math>\frac{1}{\omega\pi} e^{-\frac{(x-\xi)^2}{2\omega^2}} \int_{-\infty}^{\alpha\left(\frac{x-\xi}{\omega}\right)} e^{-\frac{t^2}{2}}\ dt</math>|
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| cdf =<math>\Phi\left(\frac{x-\xi}{\omega}\right)-2T\left(\frac{x-\xi}{\omega},\alpha\right)</math><br/><math>T(h,a)</math> is [[Owen's T function]]|
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| mean =<math>\xi + \omega\delta\sqrt{\frac{2}{\pi}}</math> where <math>\delta = \frac{\alpha}{\sqrt{1+\alpha^2}}</math>|
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| median =<!-- to do -->|
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| mode =<!-- to do -->|
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| variance =<math>\omega^2\left(1 - \frac{2\delta^2}{\pi}\right)</math>|
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| skewness =<math>\gamma_3 = \frac{4-\pi}{2} \frac{\left(\delta\sqrt{2/\pi}\right)^3}{ \left(1-2\delta^2/\pi\right)^{3/2}}</math>|
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| kurtosis =<math>2(\pi - 3)\frac{\left(\delta\sqrt{2/\pi}\right)^4}{\left(1-2\delta^2/\pi\right)^2}</math>|
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| entropy =<!-- to do -->|
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| mgf =<math>M_X\left(t\right)=2\exp\left(\xi t+\frac{\omega^2t^2}{2}\right)\Phi\left(\omega\delta t\right)</math>|
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| char =<!-- to do -->|
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| }}
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| In [[probability theory]] and [[statistics]], the '''skew normal distribution''' is a [[continuous probability distribution]] that generalises the [[normal distribution]] to allow for non-zero [[skewness]].
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| == Definition ==
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| Let <math>\phi(x)</math> denote the standard normal [[probability density function]]
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| :<math>\phi(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}</math>
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| with the [[cumulative distribution function]] given by
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| :<math>\Phi(x) = \int_{-\infty}^{x} \phi(t)\ dt = \frac{1}{2} \left[ 1 + \operatorname{erf} \left(\frac{x}{\sqrt{2}}\right)\right]</math>
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| where '''erf''' is the [[error function]]. Then the probability density function of the skew-normal distribution with parameter α is given by
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| :<math>f(x) = 2\phi(x)\Phi(\alpha x). \,</math>
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| This distribution was first introduced by O'Hagan and Leonard (1976).
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| To add [[location parameter|location]] and [[scale parameter|scale]] parameters to this, one makes the usual transform <math>x\rightarrow\frac{x-\xi}{\omega}</math>. One can verify that the normal distribution is recovered when <math>\alpha = 0</math>, and that the absolute value of the [[skewness]] increases as the absolute value of <math>\alpha</math> increases. The distribution is right skewed if <math>\alpha>0</math> and is left skewed if <math>\alpha<0</math>. The probability density function with location <math>\xi</math>, scale <math>\omega</math>, and parameter <math>\alpha</math> becomes
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| :<math>f(x) = \frac{2}{\omega}\phi\left(\frac{x-\xi}{\omega}\right)\Phi\left(\alpha \left(\frac{x-\xi}{\omega}\right)\right). \,</math>
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| Note, however, that the skewness of the distribution is limited to the interval <math>(-1,1)</math>.
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| ==Estimation==
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| [[Maximum likelihood]] estimates for <math>\xi</math>, <math>\omega</math>, and <math>\alpha</math> can be computed numerically, but no closed-form expression for the estimates is available unless <math>\alpha=0</math>. If a closed-form expression is needed, the [[Method of moments (statistics)|method of moments]] can be applied to estimate <math>\alpha</math> from the sample skew, by inverting the skewness equation. This yields the estimate
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| :<math>|\delta| = \sqrt{\frac{\pi}{2} \frac{ |\hat{\gamma}_3|^{\frac{2}{3}} }{|\hat{\gamma}_3|^{\frac{2}{3}}+((4-\pi)/2)^\frac{2}{3}}}</math>
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| where <math>\delta = \frac{\alpha}{\sqrt{1+\alpha^2}}</math>, and <math>\hat{\gamma}_3</math> is the sample skew. The sign of <math>\delta</math> is the same as the sign of <math>\hat{\gamma}_3</math>. Consequently, <math>\hat{\alpha} = \delta/\sqrt{1-\delta^2}</math>.
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| The maximum (theoretical) skewness is obtained by setting <math>{\delta = 1}</math> in the skewness equation, giving <math>\gamma_3 \approx 0.9952717</math>. However it is possible that the sample skewness is larger, and then <math>\alpha</math> cannot be determined from these equations. When using the method of moments in an automatic fashion, for example to give starting values for maximum likelihood iteration, one should therefore let (for example) <math>|\hat{\gamma}_3| = \min(0.99, |(1/n)\sum{((x_i-\bar{x})/s)^3}|)</math>.
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| ==See also==
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| * [[Normal distribution]]
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| * [[Generalized normal distribution]]
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| * [[Log-normal distribution]]
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| * [[Skewness]]
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| ==References==
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| * {{cite journal |last=Azzalini |first=A. |authorlink= |coauthors= |year=1985 |title=A class of distributions which includes the normal ones|journal=Scandinavian Journal of Statistics |volume=12 |issue= |pages=171–178}}
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| * O'Hagan, A. and Leonard, T. (1976). Bayes estimation subject to uncertainty about parameter constraints. Biometrika, 63, 201-202.
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| ==External links==
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| * [http://azzalini.stat.unipd.it/SN/Intro/intro.html A very brief introduction to the skew-normal distribution]
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| * [http://azzalini.stat.unipd.it/SN/ The Skew-Normal Probability Distribution (and related distributions, such as the skew-t)]
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| * [http://people.sc.fsu.edu/~burkardt/cpp_src/owens/owens.html OWENS: Owen's T Function]
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| * [http://dahoiv.net/master/index.html Closed-skew Distributions - Simulation, Inversion and Parameter Estimation]
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| {{ProbDistributions|continuous-infinite}}
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| {{Statistics|hide}}
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| {{DEFAULTSORT:Skew Normal Distribution}}
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| [[Category:Continuous distributions]]
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| [[Category:Probability distributions]]
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Some take advantage of the like to play basketball as you,how a person choice your basketball golf shoes?I think many more choise the air jordan,as you?Yeah,maybe you may not,but I know simple . like this method.
LaBron James was named since the NBA Rookie from the year just passed within 2003-04 as well as named the actual NBA best player last year, 10 as well as 2012 air jordan shoes . Lebron James net worth originates from his handler's the Nba. He's won each All-NBA choice and All-Star as well as every every session because july 2004. He's been included sort of a member of your USA nationwide basketball group who successful a bronze medal inside of 2004 Olympics along along with a gold medal in the 2008 Olympic games.
These shoes have turned into a household name and Nike caters to each types of shoes - both formal wear as well as casual wear. You different styles and they keep adding day by day. Nike shoes are worth every penny. The footwear are also equally durable and lend comfort. Many celebrities endorse these shoes and system another major reason for their popularity. The sneakers are you can get in all areas the world and and are avalable at leading stockists and distributors.
The air jordan 13 is often a high quality sneaker which become loved by many sportsmen and specifically those who play basketball. These also classified and worn as casual wear, fitted with a couple of jeans. They are popular as these fall under Michael Jordans line of trainers and he was wearing the pair when he scored 1st ever double three-peat.
Bearing from heart the two certainties of Baby Footwear Science, it looks like fitting (and rather cute) that Nike has created a range of Air Jordan shoes for infants. These shoes are created using the better of sports technology precision, and take under consideration the needs of developing babies.
You end up being very careful in selecting the shoes by checking every one of the used on shoes. Associated with brand company will never compromise for that materials become used for manufacturing these sneakers. Being with the safer side, it is certainly wise stop the bidding on any third party e-commerce website while searching for a set of Air Nike air jordan. For all the real shoe lovers,getting a pair of jordan sneaker will be worth in spite of considering the expense of of these footwear. In fact these shoes can be considered as an asset.
If you are you looking for more info regarding chaussure air jordan pas cher check out our website.