(Difference between revisions)
 Revision as of 19:45, 6 November 2007 (view source)IvoDinov (Talk | contribs)m (→Properties)← Older edit Revision as of 20:32, 6 November 2007 (view source)IvoDinov (Talk | contribs) m Newer edit → Line 10: Line 10:
(vertical scale) $\alpha = {12 \over \left ( b-a \right )^3}$.
(vertical scale) $\alpha = {12 \over \left ( b-a \right )^3}$.
- + More information about U-quadratic, and other continuous distribution functions, is available at [http://en.wikipedia.org/wiki/UQuadratic_distribution Wikipedia]. ===Properties=== ===Properties===

## Contents

### 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) $\alpha = {12 \over \left ( b-a \right )^3}$.

### Properties

• Support Parameters: $a < b \in (-\infty,\infty)$
• Scale/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: ${3 \over 20} (b-a)^2$
• Skewness: 0 (distribution is symmetric around the mean)
• Kurtosis: ${3 \over 112} (b-a)^4$

### 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. 