Talk:Johnson SU distribution

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Properties of the distribution[edit]

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)