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

$f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b], a < b$ ,

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) $\alpha = {3 \over 2 \left ( b-a \right )^3}$ .

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: ${\alpha \over 5} \left ( (b-\beta)^5 - (a-\beta)^5 \right )$
Skewness: TBD
Kurtosis: TBD
MGF: TBD

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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UQuadraticDistribuionAbout

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About_pages_for_SOCR_Distributions - U-Quadratic Distribution

Description

Properties

Interactive U Quadratic Distribution

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