AP Statistics Curriculum 2007 Johnson SB

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===Johnson SB Distribution===
===Johnson SB Distribution===
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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.
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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>
'''PDF''': <br>

Current revision as of 22:42, 18 July 2011

Contents

General Advance-Placement (AP) Statistics Curriculum - Johnson SB Distribution

Johnson SB Distribution

The Johnson SB distribution is related to the normal distribution. Four parameters are needed: Γ, δ, λ, ε . It is a continuous distribution defined on bounded range  \epsilon \leq x \leq \epsilon + \lambda , and the distribution can be symmetric or asymmetric.

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

CDF:
 F(x) = \Phi(\gamma + \delta ln \tfrac{z}{1-z}), where  z = \tfrac{x-\epsilon}{\lambda}

Moments:
Moments for this distribution do not have a simple expression.

Applications

\cdot Epidemiology: http://www.bvsde.paho.org/bvsacd/cd47/data.pdf

\cdot 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




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