UQuadraticDistribuionAbout
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* Skewness: 0 (distribution is symmetric around the mean) | * Skewness: 0 (distribution is symmetric around the mean) | ||
* Kurtosis: <math> {3 \over 112} (b-a)^4 </math> | * Kurtosis: <math> {3 \over 112} (b-a)^4 </math> | ||
+ | * Moment Generating Function: <math>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 }</math> | ||
+ | * Characteristic Function: <math>{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 }</math> | ||
===Interactive U Quadratic Distribution=== | ===Interactive U Quadratic Distribution=== |
Revision as of 20:03, 8 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
More information about U-quadratic, and other continuous distribution functions, is available at Wikipedia.
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:
- Moment Generating Function:
- Characteristic Function:
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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