TECHNOLOGY OVERVIEW

Johnsons Distribution

BIS.Net Team

The Johnson distribution, like the Box-Cox distribution is the resultant distribution after applying a transformation.to normalize non-normal data.

There are two main types of Johnson’s curves, The SU (unbounded) and SB (bounded) curves. The SU distribution is a 4-parameter family of distribution with the following transformation formula.

Once transformed it is possible to fit curves, compute capability indexes and other statistics

With a probability density function of

The SB distribution has the following transformation formula

With a probability density function of

Where

The Johnson curve is applied when it is not possible to fit one of the currently known distributions. There is no guarantee that the normalization will work.