UQuadraticDistribuionAbout
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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](/socr/uploads/math/2/3/7/237b827942b590ee6636a63bd9d34231.png)
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
![\beta = {b+a \over 2}](/socr/uploads/math/5/b/b/5bb84ed0c190b47fb73f4b6538360a4f.png)
![\alpha = {12 \over \left ( b-a \right )^3}](/socr/uploads/math/6/e/4/6e4251239b2517102acf4d121b301c50.png)
Properties
- Support Parameters:
- Range/Offset Parameters:
and
- PDF:
- CDF
- Mean:
- Median:
- Modes: a and b
- Variance:
- Skewness: 0 (distribution is symmetric around the mean)
- Kurtosis:
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/uploads/thumb/8/8b/SOCR_Distributions_UQuadraticAbout_Dinov_Fig2.jpg/500px-SOCR_Distributions_UQuadraticAbout_Dinov_Fig2.jpg)
- SOCR Home page: http://www.socr.ucla.edu
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