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| {{Probability distribution
| | The certain hammering actions of an influence wrench tends to make life significantly less hard when helping to loosen stubborn crazy and items. Are you organizing to get a cordless effect wrench? Seeking for a cordless influence wrench that is inside your price range would call for that you do a bit of research on-line. Check out every single and each on line shop that sells influence wrenches and evaluate the prices from one retailer to an additional. You get far more torque and a lot much more power Makita 9911 Belt Sander Opinions from a cordless influence wrench than a power drill and the price tag is generally about the same. I'm looking to buy a excellent, dependable cordless impact wrench.<br><br>I would like to see an update this summer season on this report to contain Snap On's new supplying, the CT7850 - which supposedly ups the torque to 450ft-lbs. Also, for a reference, to measure a pneumatic influence wrench. The House Depot delivers extra than two,000 Eco Options Makita 4x24 Belt Sander Critiques solutions on line and in retailer that can assist you save funds and are improved alternatives for the atmosphere. Please go to your nearest Property Depot place for details. If you want an effect to be dependable on keep on searching.<br><br>If you require a wrench that you can use for your household, a 12V impact wrench may be all you have to have. But just to be clear, the 12V cordless version may possibly be the lowest voltage but this does not imply that this device is weak. It can nevertheless do all the tasks that are [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=anticipated&gs_l=news anticipated] from any typical impact wrench. For this model of cordless influence wrench, you can count on to spend about $60 to as considerably as $800. Web-sites like� are really useful in a search for the excellent cordless influence wrench.<br><br>You need to be confident also that acquiring and obtaining the Neiko 24 Volt Cordless Impact Wrench With 350 Ft Lbs Torque can assistance you appear greater. If you enjoyed this [http://Www.Google.com/search?q=short+article&btnI=lucky short article] and you would certainly such as to receive additional details concerning Belt Sander Testimonials 2010, [http://www.bestoscillatingtoolreviews.com/belt-sander-reviews-find-the-best-model/ Get the facts], kindly browse through the site. That material is what absorbs the strike influence and focuses the power of the blow on a distinct point. An open-end wrench grips an item from each sides, with the front finish open in order to place the tool on a nut. By fully enclosing a nut, this wrench offers additional leverage.<br><br>Weighing only two.3lbs, the tool is comfortable to use for lengthy periods of time in and virtually any position or environment, and with 3 LED lights at the front of the tool, the wrench provides an successfully shadowless workspace for visibility from morning to night and each and every awkward spot in among. These days there is a wide variety of influence wrenches aimed at the house mechanic. For an air wrench that implies your compressor and lines will need to be delivering 90 PSI.<br><br>Harbor Freight Tools tends to make no representation or warranty of any sort by like this video on its web page. Founded in 1977, Harbor Freight Tools is the leading discount tool retailer in the U.S. selling excellent good quality tools at "ridiculously low costs" in over 500 retailers nationwide and on its site Harbor Freight Tools stocks over 7,000 things in categories which includes automotive, air and energy tools, shop gear and hand tools. Sold the lot for about $220 on ebay. The M18 Cordless 1/2in. |
| | name = multivariate stable
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| | type = multivariate
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| | pdf_image = [[File:Mv stable.png|220px]]<br/> <small>Heatmap showing a Multivariate (bivariate) stable distribution with ''α'' = 1.1</small>
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| | cdf_image =
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| | parameters = <math>\alpha \in (0,2]</math> — [[exponent]]<br/><math>\delta \in \mathbb{R}^d</math> - shift/location vector<br><math>\Lambda(s)</math> - a spectral finite measure on the sphere
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| | support = <math>u \in \mathbb{R}^d</math>
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| | pdf = (no analytic expression)
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| | cdf = (no analytic expression)
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| | mean =
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| | median =
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| | mode =
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| | variance = Infinite when <math>\alpha < 2</math>
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| | skewness =
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| | kurtosis =
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| | entropy =
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| | mgf =
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| | char = see text
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| }}
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| The '''multivariate stable distribution''' is a multivariate [[probability distribution]] that is a multivariate generalisation of the univariate [[stable distribution]]. The multivariate stable distribution defines linear relations between [[stable distribution]] marginals.{{clarify|date=January 2011}} In the same way as for the univariate case, the distribution is defined in terms of its [[characteristic function (probability theory)|characteristic function]].
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| The multivariate stable distribution can also be thought as an extension of the [[multivariate normal distribution]]. It has parameter, ''α'', which is defined over the range 0 < ''α'' ≤ 2, and where the case ''α'' = 2 is equivalent to the multivariate normal distribution. It has an additional skew parameter that allows for non-symmetric distributions, where the [[multivariate normal distribution]] is symmetric.
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| == Definition ==
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| Let <math> \mathbb{S} </math> be the unit sphere in <math>\mathbb R^d : \mathbb{S} = \{u \in \mathbb R^d : |u| = 1\}</math>. A [[random vector]], <math> X </math>, has a multivariate stable distribution - denoted as <math>X \sim S(\alpha, \Lambda, \delta)</math> -, if the joint characteristic function of <math>X</math> is<ref>J. Nolan, Multivariate stable densities and distribution functions: general and elliptical case, BundesBank Conference, Eltville, Germany, 11 November 2005. See also http://academic2.american.edu/~jpnolan/stable/stable.html</ref>
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| : <math>\operatorname{E} \exp(u^T X) = \exp \left\{-\int \limits_{s \in \mathbb S}\left\{|u^Ts|^\alpha + i \nu (u^Ts, \alpha) \right\} \, \Lambda(ds) + i u^T\delta\right\}</math>
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| where 0 < ''α'' < 2, and for <math> y\in\mathbb R</math>
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| :<math>\nu(y,\alpha) =\begin{cases} -\mathbf{sign}(y) \tan(\pi \alpha / 2)|y|^\alpha & \alpha \ne 1, \\
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| (2/\pi)y \ln |y| & \alpha=1. \end{cases}</math>
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| This is essentially the result of Feldheim,<ref>Feldheim, E. (1937). Etude de la stabilité des lois de probabilité . Ph. D. thesis, Faculté des Sciences de Paris, Paris, France.</ref> that any stable random vector can be characterized by a spectral measure <math>\Lambda</math> (a finite measure on <math>\mathbb S</math>) and a shift vector <math>\delta \in \mathbb R^d</math>.
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| == Parametrization using projections==
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| Another way to describe a stable random vector is in terms of projections. For any vector <math> u </math>, the projection <math>u^TX</math> is univariate <math>\alpha-</math>stable with some skewness <math>\beta(u)</math>, scale <math>\gamma(u)</math> and some shift <math>\delta(u)</math>. The notation <math>X \sim S(\alpha,\beta(\cdot),\gamma(\cdot),\delta(\cdot))</math> is used if <math>u^TX</math> is stable with
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| <math>u^TX \sim s(\alpha,\beta(\cdot),\gamma(\cdot),\delta(\cdot))</math>
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| for every <math>u \in R^d</math>. This is called the projection parameterization.
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| The spectral measure determines the projection parameter functions by:
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| : <math>\gamma(u) =
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| \int_{s \in \mathbb{S}} |u^Ts|^\alpha \Lambda(ds)
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| </math>
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| : <math>
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| \beta(u) = \int_{s \in \mathbb{S}}|u^Ts|^\alpha \mathbf{sign}(u^Ts)\Lambda(ds)
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| </math>
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| : <math>\delta(u)=\begin{cases}u^T \delta & \alpha \ne 1\\u^T \delta -\int_{s \in \mathbb{S}}\tfrac{\pi}{2} u^Ts \ln|u^Ts|\Lambda(ds)&\alpha=1\end{cases}</math>
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| ==Special cases==
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| There are four special cases where the multivariate [[characteristic function (probability theory)|characteristic function]] takes a simpler form. Define the characteristic function of a stable marginal as
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| : <math>\omega(y|\alpha,\beta) =
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| \begin{cases}|y|^\alpha\left[1-i \beta(\tan \tfrac{\pi\alpha}{2})\mathbf{sign}(y)\right]& \alpha \ne 1\\
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| |y|\left[1+i \beta \tfrac{2}{\pi} \mathbf{sign}(y)\ln |y|\right] & \alpha = 1\end{cases}
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| </math>
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| ===Isotropic multivariate stable distribution===
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| The characteristic function is
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| <math>E \exp(i u^T X)=\exp\{-\gamma_0^\alpha+i u^T \delta)\}</math>
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| The spectral measure is continuous and uniform, leading to radial/isotropic symmetry.<ref>User manual for STABLE 5.1 Matlab version, Robust Analysis Inc., http://www.RobustAnalysis.com</ref>
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| ===Elliptically contoured multivariate stable distribution===
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| Elliptically contoured m.v. stable distribution is a special symmetric case of the multivariate stable distribution.
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| If X is <math>\alpha</math>-stable and elliptically contoured, then it has joint [[characteristic function (probability theory)|characteristic function]]
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| <math>E \exp(i u^T X)=\exp\{-(u^T\Sigma u)^{\alpha/2}+i u^T \delta)\}</math>
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| for some positive definite matrix <math>\Sigma</math> and shift vector <math>\delta \in R^d</math>.
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| Note the relation to characteristic function of the [[multivariate normal distribution]]: <math>E \exp(i u^T X)=\exp\{-(u^T\Sigma u)+i u^T \delta)\}</math>.
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| In other words, when ''α'' = 2 we get the characteristic function of the multivariate normal distribution.
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| ===Independent components===
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| The marginals are independent with <math>X_j \sim S(\alpha, \beta_j, \gamma_j, \delta_j)</math>, then the
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| characteristic function is
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| : <math>E \exp(i u^T X) = \exp\left\{-\sum_{j=1}^m \omega(u_j|\alpha,\beta_j)\gamma_j^\alpha +i u^T \delta)\right\}</math>
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| {|
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| |-
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| |[[File:Mv indp.png|Mv indp|220px]]<br/> <small>Heatmap showing a multivariate (bivariate) independent stable distribution with ''α'' = 1</small> ||
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| [[File:Mv indp2.png|Mv indp2|220px]]<br/><small>Heatmap showing a multivariate (bivariate) independent stable distribution with ''α'' = 2</small>.
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| |}
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| ===Discrete===
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| If the spectral measure is discrete with mass <math>\lambda_j</math> at <math>s_j \in \mathbb{S},j=1,\ldots,m</math>
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| the characteristic function is | |
| : <math>E \exp(i u^T X)= \exp\left\{-\sum_{j=1}^m \omega(u^Ts_j|\alpha,1)\gamma_j^\alpha +i u^T \delta)\right\}</math>
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| == Linear properties ==
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| if <math>X \sim S(\alpha, \beta(\cdot), \gamma(\cdot), \delta(\cdot))
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| </math> is d-dim, and A is a m x d matrix, <math>b \in \mathbb{R}^m</math>
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| then AX + b is m dim. <math>\alpha</math>-stable with scale function <math>\gamma(A^T\cdot)</math>
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| , skewness function <math>\beta(A^T\cdot)</math>,
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| and location function <math>\delta(A^T\cdot) + b^T\cdot</math>
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| == Inference in the independent component model ==
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| Recently<ref>D. Bickson and C. Guestrin. Inference in linear models with multivariate heavy-tails. In Neural Information Processing Systems (NIPS) 2010, Vancouver, Canada, Dec. 2010. http://www.cs.cmu.edu/~bickson/stable/</ref> it was shown how to compute inference in closed-form in a linear model (or equivalently a [[factor analysis]] model),involving independent component models.
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| More specifically, let <math>X_i \sim S(\alpha, \beta_{x_i}, \gamma_{x_i}, \delta_{x_i}), i=1,\ldots,n</math> be a set of i.i.d. unobserved univariate drawn from a [[stable distribution]]. Given a known linear relation matrix A of size <math>n \times n</math>, the observation <math>Y_i = \sum_{i=1}^n A_{ij}X_j</math> are assumed to be distributed as a convolution of the hidden factors <math>X_i</math>. <math>Y_i = S(\alpha, \beta_{y_i}, \gamma_{y_i}, \delta_{y_i})</math>. The inference task is to compute the most probable <math>X_i</math>, given the linear relation matrix A and the observations <math>Y_i</math>. This task can be computed in closed-form in O(''n''<sup>3</sup>).
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| An application for this construction is [[multiuser detection]] with stable, non-Gaussian noise.
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| ==Resources==
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| * Mark Veillette's stable distribution matlab package http://www.mathworks.com/matlabcentral/fileexchange/37514
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| * The plots in this page where plotted using Danny Bickson's inference in linear-stable model Matlab package: http://www.cs.cmu.edu/~bickson/stable
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| ==Notes==
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| {{Reflist}}
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| {{ProbDistributions|multivariate}}
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| {{DEFAULTSORT:Multivariate Stable Distribution}}
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| [[Category:Multivariate continuous distributions]]
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| [[Category:Probability distributions with non-finite variance]]
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| [[Category:Probability distributions]]
| |
The certain hammering actions of an influence wrench tends to make life significantly less hard when helping to loosen stubborn crazy and items. Are you organizing to get a cordless effect wrench? Seeking for a cordless influence wrench that is inside your price range would call for that you do a bit of research on-line. Check out every single and each on line shop that sells influence wrenches and evaluate the prices from one retailer to an additional. You get far more torque and a lot much more power Makita 9911 Belt Sander Opinions from a cordless influence wrench than a power drill and the price tag is generally about the same. I'm looking to buy a excellent, dependable cordless impact wrench.
I would like to see an update this summer season on this report to contain Snap On's new supplying, the CT7850 - which supposedly ups the torque to 450ft-lbs. Also, for a reference, to measure a pneumatic influence wrench. The House Depot delivers extra than two,000 Eco Options Makita 4x24 Belt Sander Critiques solutions on line and in retailer that can assist you save funds and are improved alternatives for the atmosphere. Please go to your nearest Property Depot place for details. If you want an effect to be dependable on keep on searching.
If you require a wrench that you can use for your household, a 12V impact wrench may be all you have to have. But just to be clear, the 12V cordless version may possibly be the lowest voltage but this does not imply that this device is weak. It can nevertheless do all the tasks that are anticipated from any typical impact wrench. For this model of cordless influence wrench, you can count on to spend about $60 to as considerably as $800. Web-sites like� are really useful in a search for the excellent cordless influence wrench.
You need to be confident also that acquiring and obtaining the Neiko 24 Volt Cordless Impact Wrench With 350 Ft Lbs Torque can assistance you appear greater. If you enjoyed this short article and you would certainly such as to receive additional details concerning Belt Sander Testimonials 2010, Get the facts, kindly browse through the site. That material is what absorbs the strike influence and focuses the power of the blow on a distinct point. An open-end wrench grips an item from each sides, with the front finish open in order to place the tool on a nut. By fully enclosing a nut, this wrench offers additional leverage.
Weighing only two.3lbs, the tool is comfortable to use for lengthy periods of time in and virtually any position or environment, and with 3 LED lights at the front of the tool, the wrench provides an successfully shadowless workspace for visibility from morning to night and each and every awkward spot in among. These days there is a wide variety of influence wrenches aimed at the house mechanic. For an air wrench that implies your compressor and lines will need to be delivering 90 PSI.
Harbor Freight Tools tends to make no representation or warranty of any sort by like this video on its web page. Founded in 1977, Harbor Freight Tools is the leading discount tool retailer in the U.S. selling excellent good quality tools at "ridiculously low costs" in over 500 retailers nationwide and on its site Harbor Freight Tools stocks over 7,000 things in categories which includes automotive, air and energy tools, shop gear and hand tools. Sold the lot for about $220 on ebay. The M18 Cordless 1/2in.