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Johnson SU distribution : ウィキペディア英語版
Johnson SU distribution

\frac)^}}e^(\gamma+\delta \sinh^(\frac))^}
| cdf = \Phi (\gamma + \delta \sinh^(\frac))
| mean = \xi - \lambda \exp} \sinh(\frac)
| median =
| mode =
| variance = \frac(\exp-1)(\exp\cosh)}+1)
| skewness =
| kurtosis =
| entropy =
| pgf =
| mgf =
| char =
}}
The Johnson S_U distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949.〔Johnson, N. L. (1949) Systems of frequency curves generated by methods of translation. ''Biometrika'' 36: 149–176 〕 Johnson proposed it as a transformation of the normal distribution:〔N.L. Johnson, Table to facilitate fitting SU frequency curves, Biometrika 1949〕
z=\gamma+\delta \sinh^ (\frac)
Where z \sim \mathcal(0,1)
==Generation of random variables==

Let ''U'' be a random variable that is uniformly distributed on the unit interval (). Johnson S_U random variables can be generated from ''U'' as follows:
: x = \lambda \sinh\left( \frac \right) + \xi
where Φ is the cumulative distribution function of the normal distribution.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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