Difference between revisions of "UQuadraticDistribuionAbout"

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===Interactive U Quadratic Distribution===
 
===Interactive U Quadratic Distribution===
You can see the interactive ''U Quadratic'' distribution by going to [http://socr.ucla.edu/htmls/SOCR_Distributions.html SOCR Distributions] and selecting from the drop down list of distributions ''U Quadratic''. Then follow the '''Help''' instructions to dynamically set parameters, compute critical and probability values using the mouse and keyboard.
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You can see the interactive ''U Quadratic'' distribution by going to [http://socr.ucla.edu/htmls/dist/UQuadratic_Distribution.html SOCR Distributions] and selecting from the drop down list of distributions ''U Quadratic''. Then follow the '''Help''' instructions to dynamically set parameters, compute critical and probability values using the mouse and keyboard.
  
 
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* SOCR Home page: http://www.socr.ucla.edu
 
* SOCR Home page: http://www.socr.ucla.edu
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* [http://en.wikipedia.org/wiki/U-quadratic_distribution U-quadratic distribution at Wikipedia]
  
 
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=UQuadraticDistribuionAbout}}
 
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=UQuadraticDistribuionAbout}}

Latest revision as of 14:15, 28 December 2009

About_pages_for_SOCR_Distributions - U-Quadratic Distribution

Description

SOCR Distributions UQuadraticAbout Dinov Fig1.jpg

The U quadratic distribution is defined by the following density function

\( f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b], a < b\),

where the relation between the two pairs of parameters (domain-support, a and b) and (range/offset \(\alpha\) and \(\beta\)) are given by the following two equations

(gravitational balance center) \(\beta = {b+a \over 2}\), and
(vertical scale) \(\alpha = {12 \over \left ( b-a \right )^3}\).

More information about U-quadratic, and other continuous distribution functions, is available at Wikipedia.

Properties

  • Support Parameters\[a < b \in (-\infty,\infty)\]
  • Scale/Offset Parameters\[\alpha \in (0,\infty)\] and \(\beta \in (-\infty,\infty)\)
  • PDF\[f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b]\]
  • CDF \(F(x)={\alpha \over 3} \left ( (x - \beta)^3 + (\beta - a)^3 \right ), \forall x \in [a , b]\)
  • Mean\[{a+b \over 2}\]
  • Median\[{a+b \over 2}\]
  • Modes\[a \] and \( b \)
  • Variance\[ {3 \over 20} (b-a)^2 \]
  • Skewness: 0 (distribution is symmetric around the mean)
  • Kurtosis\[ {3 \over 112} (b-a)^4 \]
  • Moment Generating Function\[M_x(t)= {-3\left(e^{at}(4+(a^2+2a(-2+b)+b^2)t)- e^{bt} (4 + (-4b + (a+b)^2)t)\right) \over (a-b)^3 t^2 }\]
  • Characteristic Function\[{3i\left(e^{iat}(-4i+(a^2+2a(-2+b)+b^2)t)+ e^{ibt} (4i - (-4b + (a+b)^2)t)\right) \over (a-b)^3 t^2 }\]

Interactive U Quadratic Distribution

You can see the interactive U Quadratic distribution by going to SOCR Distributions and selecting from the drop down list of distributions U Quadratic. Then follow the Help instructions to dynamically set parameters, compute critical and probability values using the mouse and keyboard.

SOCR Distributions UQuadraticAbout Dinov Fig2.jpg



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