Johnsons Distribution

The BIS.Net Team BIS.Net Team

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

Johnsons Distribution

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

Johnson formula 1

With a probability density function of

Johnson formula 2

The SB distribution has the following transformation formula

Johnson formula 3

With a probability density function of

Johnson formula 4


Johnson formula 6

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.

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