Transform (version 1.0)

bdTransform: Bickel-Docksum Transformation for Normality

Description

bdTransform performs Bickel-Docksum transformation for normality of a variable and provides graphical analysis.

Usage

bdTransform(data, lambda = seq(0.01,6,0.01), plot = TRUE, alpha = 0.05, 
  verbose = TRUE)

Value

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

method

method to estimate Bickel-Docksum transformation parameter

lambda.hat

estimate of Bickel-Docksum 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 (0.01,6) 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 Bickel-Docksum power transformation is defined by:

$$y' = \frac{|y|^\lambda Sign(y)-1}{\lambda} \mbox{ , if $\lambda > 0$} $$

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.

Bickel, P.J., Doksum, K.A. (1981). An Analysis of Transformations Revisited. Journal of the American Statistical Association, 76:374, 296--311.

Examples

data <- cars$dist

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