AP Statistics Curriculum 2007 Johnson SB
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\[\Gamma\], \(\delta\), \(\lambda\), \(\epsilon\) . It is a continuous distribution defined on bounded range \( \epsilon \leq x \leq \epsilon + \lambda \), and the distribution can be symmetric or asymmetric.
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\( f(x) = \tfrac{\delta}{\lambda\sqrt{2\pi} z(1-z)} exp(-\tfrac{1}{2}(\gamma + \delta ln(\tfrac{z}{1-z}))^2)\), 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
- SOCR Home page: http://www.socr.ucla.edu
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