Johnson's SU-distribution
The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. Johnson proposed it as a transformation of the normal distribution:
where.Let U be a random variable that is uniformly distributed on the unit interval . Johnson's SU random variables can be generated from U as follows:
where Φ is the cumulative distribution function of the normal distribution.Johnson's ''SB''-distribution
firstly proposes the transformation :
where.
Johnson's SB random variables can be generated from U as follows:
The SB-distribution is convenient to Platykurtic distributions.
To simulate SU, sample of code for its density and cumulative density function is available Applications
Johnson's -distribution has been used successfully to model asset returns for portfolio management.
