AP Statistics Curriculum 2007 Johnson SB

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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.

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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