UQuadraticDistribuionAbout
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===Properties=== | ===Properties=== | ||
* Support Parameters: <math>a < b \in (-\infty,\infty)</math> | * Support Parameters: <math>a < b \in (-\infty,\infty)</math> | ||
- | * | + | * Scale/Offset Parameters: <math>\alpha \in (0,\infty)</math> and <math>\beta \in (-\infty,\infty)</math> |
* PDF: <math>f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b]</math> | * PDF: <math>f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b]</math> | ||
* CDF <math>F(x)={\alpha \over 3} \left ( (x - \beta)^3 + (\beta - a)^3 \right ), \forall x \in [a , b]</math> | * CDF <math>F(x)={\alpha \over 3} \left ( (x - \beta)^3 + (\beta - a)^3 \right ), \forall x \in [a , b]</math> |
Revision as of 19:45, 6 November 2007
Contents |
About_pages_for_SOCR_Distributions - U-Quadratic Distribution
Description
The U quadratic distribution is defined by the following density function
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
Properties
- Support Parameters:
- Scale/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 Home page: http://www.socr.ucla.edu
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