AP Statistics Curriculum 2007 Johnson SB - Revision history

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JayZzz: /* Johnson SB Distribution */

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‎Johnson SB Distribution

JayZzz at 04:59, 4 July 2011

2011-07-04T04:59:12Z

JayZzz: Created page with '== General Advance-Placement (AP) Statistics Curriculum - Johnson SB Distribution== ===Johnson SB Distribution=== The Johnson SB distribution …'

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Created page with '== General Advance-Placement (AP) Statistics Curriculum - Johnson SB Distribution== ===Johnson SB Distribution=== The Johnson SB distribution …'

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==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Johnson SB Distribution==

===Johnson SB Distribution===
The Johnson SB distribution is related to the [http://en.wikipedia.org/wiki/Normal_distribution normal distribution]. Four parameters are needed: <math>\Gamma</math>, <math>\delta</math>, <math>\lambda</math>, <math>\epsilon</math> . It is a continuous distribution defined on bounded range <math> \epsilon \leq x \leq \epsilon + \lambda </math>, and the distribution can be symmetric or asymmetric.

'''PDF''': <br>
<math> f(x) = \tfrac{\delta}{\lambda\sqrt{2\pi} z(1-z)} exp(-\tfrac{1}{2}(\gamma + \delta ln(\tfrac{z}{1-z}))^2)</math>, where <math>z \equiv \tfrac{x-\zeta}{\lambda}</math>

'''CDF''': <br>
<math> F(x) = \Phi(\gamma + \delta ln \tfrac{z}{1-z})</math>, where <math> z = \tfrac{x-\epsilon}{\lambda}</math>

'''Moments''': <br>
Moments for this distribution do not have a simple expression.

===Applications===
<math>\cdot</math> Epidemiology: http://www.bvsde.paho.org/bvsacd/cd47/data.pdf

<math>\cdot</math> Forrestry: http://cms1.gre.ac.uk/conferences/iufro/FMA/SB_Plot_Minimum1.pdf

===SOCR Links===
http://www.distributome.org/ -> SOCR -> Distributions -> Johnson Special Bounded (SB) Distribution

http://www.distributome.org/ -> SOCR -> Functors -> Johnson Special Bounded (SB) Distribution

SOCR Docs: http://www.socr.ucla.edu/docs/edu/ucla/stat/SOCR/distributions/JohnsonSBDistribution.html

SOCR Calculator: http://socr.ucla.edu/htmls/dist/JohnsonSBDistribution.html

===See Also===
http://www.mathwave.com/articles/johnson_sb_distribution.html

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

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 ===Johnson SB Distribution===
-The Johnson SB distribution is related to the [http://en.wikipedia.org/wiki/Normal_distribution normal distribution]. Four parameters are needed: <math>\Gamma</math>, <math>\delta</math>, <math>\lambda</math>, <math>\epsilon</math>  . It is a continuous distribution defined on bounded range <math> \epsilon \leq x \leq \epsilon + \lambda </math>, and the distribution can be symmetric or asymmetric.
+The Johnson SB distribution is related to the [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Normal_Std normal distribution]. Four parameters are needed: <math>\Gamma</math>, <math>\delta</math>, <math>\lambda</math>, <math>\epsilon</math>  . It is a continuous distribution defined on bounded range <math> \epsilon \leq x \leq \epsilon + \lambda </math>, and the distribution can be symmetric or asymmetric.
 '''PDF''': <br>