# AP Statistics Curriculum 2007 Johnson SB

(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)

## 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