Probability distributions, of widely differing shapes, that can be obtained by simple transformations of the standard normal distribution. The relationship to the normal distribution makes it easy to calculate, for example, a tail probability. The entire family is defined by , where α and β are constants, g is a function, Z is a standard normal random variable and Y is a Johnson random variable.
There are three classes of Johnson distributions, referred to as the SU, SB, and SL classes, which result from different choices for the function g(x). In the order given, for a variable x, the functions are . The last case gives a type of lognormal distribution.
Subjects: Probability and Statistics.