Transform (version 1.0)

mdTransform: Modulus Transformation for Normality

Description

mdTransform performs Modulus transformation for normality of a variable and provides graphical analysis.

Usage

mdTransform(data, lambda = seq(-3,3,0.01), plot = TRUE, alpha = 0.05, 
  verbose = TRUE)

Value

A list with class "md" containing the following elements:

method

method to estimate Modulus transformation parameter

lambda.hat

estimate of Modulus transformation parameter

statistic

Shapiro-Wilk test statistic for transformed data

p.value

Shapiro-Wilk test p.value for transformed data

alpha

level of significance to assess normality

tf.data

transformed data set

var.name

variable name

Arguments

data

a numeric vector of data values.

lambda

a vector which includes the sequence of candidate lambda values. Default is set to (-3,3) with increment 0.01.

plot

a logical to plot histogram with its density line and qqplot of raw and transformed data. Defaults plot = TRUE.

alpha

the level of significance to check the normality after transformation. Default is set to alpha = 0.05.

verbose

a logical for printing output to R console.

Author

Muge Coskun Yildirim, Osman Dag

Details

Denote \(y\) the variable at the original scale and \(y'\) the transformed variable. The Modulus power transformation is defined by:

$$y' = \left\{ \begin{array}{ll} Sign(y)\frac{(|y|+1)^\lambda-1}{\lambda} \mbox{ , if $\lambda \neq 0$} \cr Sign(y) \log{(|y|+1)} \mbox{ , if $\lambda = 0$} \end{array} \right. $$

References

Asar, O., Ilk, O., Dag, O. (2017). Estimating Box-Cox Power Transformation Parameter via Goodness of Fit Tests. Communications in Statistics - Simulation and Computation, 46:1, 91--105.

John, J., Draper, N.R. (1980). An Alternative Family of Transformations. Journal of the Royal Statistical Society Series C: Applied Statistics, 29:2, 190--7.

Examples

data <- cars$dist

library(Transform)
out <- mdTransform(data)
out$lambda.hat # the estimate of Modulus parameter based on Shapiro-Wilk test statistic 
out$p.value # p.value of Shapiro-Wilk test for transformed data 
out$tf.data # transformed data set