Log structure

The Johnson $S_{U}$ distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. It is closely related to the normal distribution.

Generation of random variables

Let U be a random variable that is uniformly distributed on the unit interval [0, 1]. Johnson $S_{U}$ random variables can be generated from U as follows:

$x=\lambda \sinh \left({\frac {1}{\sigma }}\Phi ^{-1}(U)-\gamma \right)+\chi$

where Φ is the cumulative distribution function of the normal distribution.

References

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