jtrans (version 0.2.1)

jtrans: Johnson Transformation for Normality

Description

jtrans transforms a continuous univariate vector to a random vector from standard normal distribution.

Usage

jtrans(x, test = "shapiro.test", exclude_original = TRUE, z_lim = c(0.25, 1.25), z_length = 101)

Arguments

x

the non-normal numerical data.

test

the normality test used to select fits, defaults to shapiro.test

exclude_original

whether the original data should be excluded when comparing fits.

z_lim

two values vector defining the range of the z values, defaults to 0.25 to 1.25, which is recommended by Mandraccia, Halverson and Chou (1996).

z_length

the length of the z vector, default to 101. The number of different fits estiamted in the algorithm. Set larger z.length value if you want extra precision.

Value

A list with two classes: the first one is the type of transformation used, the same as the type component, could be "sb", "su" or "sl"; The second one is "jtrans". The list containsthe following components:

original

original data.

transformed

transformed data.

type

type of transformation selected.

test

normality test used to select transformations.

z

selected z value among 101 values from 0.25 to 1.25.

eta, gamma, lambda, epsilon

transformation parameters.

p.value

the maximum p.value returned by test

Details

jtrans fits data to a set of distributions from Johnson family. A normality test is used to find the best fit by choosing the fit with maximum p.value under that given test. It returns the transformed data, the corresponding type of Johnson curve and parameter estimations.

Since the default Shapiro-Wilk test can only accept sample size between 3 and 5000, one should specify another normality test in the test parameter, generally the ad.test in the nortest package is recommended.

Sometimes, this algorithm may return poor fits. The most extreme case is that all the transformed data have smaller p.values than the original data's. In such cases, the exclude_original flag should be set to FALSE, so jtrans will return the original data as the transformed data.

References

Chou, Y. M., Polansky, A. M., & Mason, R. L. (1998). Transforming non-normal data to normality in statistical process control. Journal of Quality Technology, 30(2), 133-141.

Examples

# generate 100 non-normal data and transform it.
x <- rexp(50, .2)
jt <- jtrans(x)
jt

plot(density(x))
plot(density(jt$transformed))
qqnorm(jt$transformed)
qqline(jt$transformed)

## Not run: 
# # Using another normality test
# require(nortest)
# jtrans(x, test = "ad.test")
# ## End(Not run)