UQuadraticDistribuionAbout

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(New page: == About_pages_for_SOCR_Distributions - U-Quadratic Distribution == ===Description=== right The ''U quadrat...)
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<center>(gravitational balance center) <math>\beta = {b+a \over 2}</math>, and
<center>(gravitational balance center) <math>\beta = {b+a \over 2}</math>, and
</center>
</center>
-
<center>(vertical scale) <math>\alpha = {3 \over 2 \left ( b-a \right )^3}</math>.
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<center>(vertical scale) <math>\alpha = {12 \over \left ( b-a \right )^3}</math>.
</center>
</center>
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* Median: <math>{a+b \over 2}</math>
* Median: <math>{a+b \over 2}</math>
* Modes: <math>a </math> and <math> b </math>
* Modes: <math>a </math> and <math> b </math>
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* Variance: <math> {\alpha \over 5} \left ( (b-\beta)^5 - (a-\beta)^5 \right )</math>
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* Variance: <math> {3 \over 20} (b-a)^2 </math>
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* Skewness: TBD
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* Skewness: 0 (distribution is symmetric around the mean)
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* Kurtosis: TBD
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* Kurtosis: <math> {3 \over 112} (b-a)^4 </math>
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* MGF: TBD
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===Interactive U Quadratic Distribution===
===Interactive U Quadratic Distribution===

Revision as of 18:47, 6 November 2007

Contents

About_pages_for_SOCR_Distributions - U-Quadratic Distribution

Description

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 α and β) 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}.


Properties

  • Support Parameters: a < b \in (-\infty,\infty)
  • Range/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

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.




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