# AP Statistics Curriculum 2007 Johnson SB

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 Revision as of 04:52, 4 July 2011 (view source)JayZzz (Talk | contribs) (Created page with '== General Advance-Placement (AP) Statistics Curriculum - Johnson SB Distribution== ===Johnson SB Distribution=== The Johnson SB distribution …')← Older edit Current revision as of 22:44, 18 July 2011 (view source)JayZzz (Talk | contribs) (→Johnson SB Distribution) (One intermediate revision not shown) Line 2: Line 2: ===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: $\Gamma$, $\delta$, $\lambda$, $\epsilon$  . It is a continuous distribution defined on bounded range $\epsilon \leq x \leq \epsilon + \lambda$, and the distribution can be symmetric or asymmetric. + 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: $\Gamma$, $\delta$, $\lambda$, $\epsilon$  . It is a continuous distribution defined on bounded range $\epsilon \leq x \leq \epsilon + \lambda$, and the distribution can be symmetric or asymmetric. '''PDF''':
'''PDF''':

## 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

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

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

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