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 = { | + | <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> | ||
- | * Variance: <math> { | + | * Variance: <math> {3 \over 20} (b-a)^2 </math> |
- | * Skewness: | + | * Skewness: 0 (distribution is symmetric around the mean) |
- | * Kurtosis: | + | * Kurtosis: <math> {3 \over 112} (b-a)^4 </math> |
- | + | ||
===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
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:
- 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 Home page: http://www.socr.ucla.edu
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