# RE.Johnson: Johnson transformation In Johnson: Johnson Transformation

## Description

Johnson transform to normality using the Z family of distributions. Performs the Johnson Transformation based on the method of the percentiles. Returns the the transformed variable, the function used and de p-value of the transformation.

## Usage

 `1` ```RE.Johnson(x) ```

## Arguments

 `x` x vector of observations

## Details

The values of the Johnson Transformation Function can be obtained

## Value

The objects returned consists of the following items: function type of function used in transformation (SB,SL or SU) p-value the resulting p-value of the transformation transformed the data vector of transformed variable f.gamma, f.lambda, f.epsilon and f.eta the values of the variables in the transformation function.

## Note

Note that the transformed variable often present a good fit to the normal distribution.

## Author(s)

Edgar Santos Fernandez

## References

Chou, Youn Min; Polansky, A. M. M. R. L. (1998), "Transforming non normal data to normality in statistical process control", Journal of Quality Technology 30, 2, April.

Johnson, N. L. (1949), "Systems of Frequency Curves Generated by Methods of Translation". URL: http://www.jstor.org/stable/2332539

Slifker, J. F. & Shapiro, S. S. (1980), "The johnson system: selection and parameter estimation", Technometrics 22(2).

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# transforming to normality a random sample with beta distribution x <- rbeta(30,2,3) y <- RE.Johnson(x); print(y) # working with the transformed variable x <- runif(100) y <- RE.Johnson(x) \$transformed ; print(y) # working with the p-values x <- rgamma(100,2,1) y <- RE.Johnson(x)\$p ;print(y) ```