UQuadraticDistribuionAbout - Revision history

IvoDinov at 19:15, 28 December 2009

2009-12-28T19:15:18Z

IvoDinov at 17:56, 22 May 2009

2009-05-22T17:56:19Z

Rgidwani: Updated MGF and CF

2007-11-08T20:09:24Z

Updated MGF and CF

IvoDinov at 20:38, 6 November 2007

2007-11-06T20:38:26Z

IvoDinov: /* Properties */

2007-11-06T19:51:23Z

‎Properties

Jenny at 18:53, 6 November 2007

2007-11-06T18:53:48Z

Jenny: New page: == About_pages_for_SOCR_Distributions - U-Quadratic Distribution == ===Description=== right The ''U quadrat...

2007-11-05T19:03:23Z

New page: == About_pages_for_SOCR_Distributions - U-Quadratic Distribution == ===Description=== 400px|thumbnail|right The ''U quadrat...

New page

== [[About_pages_for_SOCR_Distributions]] - U-Quadratic Distribution ==

===Description===
[[Image:SOCR_Distributions_UQuadraticAbout_Dinov_Fig1.jpg|400px|thumbnail|right]]
The ''U quadratic distribution'' is defined by the following density function
<center><math> f(x)=\alpha \left ( x - \beta \right )^2, \forall x \in [a , b], a < b</math>, </center>
where the relation between the two pairs of parameters (domain-support, a and b) and (range/offset <math>\alpha</math> and <math>\beta</math>) are given by the following two equations
<center>(gravitational balance center) <math>\beta = {b+a \over 2}</math>, and
</center>
<center>(vertical scale) <math>\alpha = {3 \over 2 \left ( b-a \right )^3}</math>.
</center>

===Properties===
* Support Parameters: <math>a < b \in (-\infty,\infty)</math>
* Range/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>
* CDF <math>F(x)={\alpha \over 3} \left ( (x - \beta)^3 + (\beta - a)^3 \right ), \forall x \in [a , b]</math>
* Mean: <math>{a+b \over 2}</math>
* Median: <math>{a+b \over 2}</math>
* Modes: <math>a </math> and <math> b </math>
* Variance: <math> {\alpha \over 5} \left ( (b-\beta)^5 - (a-\beta)^5 \right )</math>
* Skewness: TBD
* Kurtosis: TBD
* MGF: TBD

===Interactive U Quadratic Distribution===
You can see the interactive ''U Quadratic'' distribution by going to [http://socr.ucla.edu/htmls/SOCR_Distributions.html 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.

<center>[[Image:SOCR_Distributions_UQuadraticAbout_Dinov_Fig2.jpg|500px]]</center>

<hr>
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=UQuadraticDistribuionAbout}}

@@ Line 23: / Line 23: @@
 * Skewness: 0 (distribution is symmetric around the mean)
 * Kurtosis: <math> {3 \over 112} (b-a)^4 </math>
 ===Interactive U Quadratic Distribution===

@@ Line 10: / Line 10: @@
 <center>(vertical scale) <math>\alpha = {12 \over \left ( b-a \right )^3}</math>.
 </center>
+More information about U-quadratic, and other continuous distribution functions, is available at [http://en.wikipedia.org/wiki/UQuadratic_distribution Wikipedia].
 ===Properties===

@@ Line 27: / Line 27: @@
 ===Interactive U Quadratic Distribution===
-You can see the interactive ''U Quadratic'' distribution by going to [http://socr.ucla.edu/htmls/SOCR_Distributions.html 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.
+You can see the interactive ''U Quadratic'' distribution by going to [http://socr.ucla.edu/htmls/dist/UQuadratic_Distribution.html 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.
 <center>[[Image:SOCR_Distributions_UQuadraticAbout_Dinov_Fig2.jpg|500px]]</center>
@@ Line 33: / Line 33: @@
 <hr>
 * SOCR Home page: http://www.socr.ucla.edu
-* [http://en.wikipedia.org/wiki/U-quadratic_distribution U-quadratic distribution at Wikipedia]]
+* [http://en.wikipedia.org/wiki/U-quadratic_distribution U-quadratic distribution at Wikipedia]
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=UQuadraticDistribuionAbout}}

@@ Line 14: / Line 14: @@
 ===Properties===
 * Support Parameters: <math>a < b \in (-\infty,\infty)</math>
-* Range/Offset Parameters: <math>\alpha \in (0,\infty)</math> and <math>\beta \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>
 * CDF  <math>F(x)={\alpha \over 3} \left ( (x - \beta)^3 + (\beta - a)^3 \right ), \forall x \in [a , b]</math>

@@ Line 8: / Line 8: @@
 <center>(gravitational balance center) <math>\beta = {b+a \over 2}</math>, and
 </center>
-<center>(vertical scale) <math>\alpha = {3 \over 2 \left ( b-a \right )^3}</math>.
+<center>(vertical scale) <math>\alpha = {12 \over \left ( b-a \right )^3}</math>.
 </center>
@@ Line 20: / Line 20: @@
 * Median: <math>{a+b \over 2}</math>
 * Modes: <math>a </math> and <math> b </math>
-* Variance: <math> {\alpha \over 5} \left ( (b-\beta)^5 - (a-\beta)^5 \right )</math>
+* Variance: <math> {3 \over 20} (b-a)^2 </math>
-* Skewness: TBD
+* Skewness: 0 (distribution is symmetric around the mean)
-* Kurtosis: TBD
+* Kurtosis: <math> {3 \over 112} (b-a)^4 </math>
 ===Interactive U Quadratic Distribution===