# Talk:Johnson SU distribution

WikiProject Mathematics (Rated Stub-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Stub Class
 Low Importance
Field: Probability and statistics
WikiProject Statistics (Rated Stub-class, Low-importance)

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Stub  This article has been rated as Stub-Class on the quality scale.
Low  This article has been rated as Low-importance on the importance scale.

## Properties of the distribution

The PDF of this function is is

$\frac{ \sigma } { \lambda \sqrt{2 \pi ( z^2 + 1 ) } } \exp[ - \frac{ 1 }{ 2 } ( \gamma + \sigma \sinh^{ -1 }( z )^2 ]$

where $z = \frac{ x - \chi }{ \lambda }$

The variance is

$0.5 \lambda^2 [ \exp( \sigma^{ -2 } - 1 ) ] [ \exp( \sigma^{ -2 } \cosh^2( \frac{ 2 \gamma } { \sigma } ) + 1 ]$

For reasons that I cannot currently fathom, if I try to add these to the infobox on the main page it will not accept this. I'm sure some other editor can do this. Thanks in advance. DrMicro (talk) 10:44, 6 November 2012 (UTC)