BoxCox: The Box-Cox Transformed Normal Distribution

In geoR: Analysis of Geostatistical Data

The Box-Cox Transformed Normal Distribution

Description

Functions related with the Box-Cox family of transformations. Density and random generation for the Box-Cox transformed normal distribution with mean equal to mean and standard deviation equal to sd, in the normal scale.

Usage

rboxcox(n, lambda, lambda2 = NULL, mean = 0, sd = 1)

dboxcox(x, lambda, lambda2 = NULL, mean = 0, sd = 1)

Arguments

lambda	numerical value(s) for the transformation parameter \lambda.
lambda2	logical or numerical value(s) of the additional transformation (see DETAILS below). Defaults to NULL.
n	number of observations to be generated.
x	a vector of quantiles (dboxcox) or an output of boxcoxfit (print, plot, lines).
mean	a vector of mean values at the normal scale.
sd	a vector of standard deviations at the normal scale.

Details

Denote Y the variable at the original scale and Y' the transformed variable. The Box-Cox transformation is defined by:

Y' = \left\{ \begin{array}{ll} log(Y) \mbox{ , if $\lambda = 0$} \cr \frac{Y^\lambda - 1}{\lambda} \mbox{ , otherwise} \end{array} \right.

.

An additional shifting parameter \lambda_2 can be included in which case the transformation is given by:

Y' = \left\{ \begin{array}{ll} log(Y + \lambda_2) \mbox{ , $\lambda = 0$ } \cr \frac{(Y + \lambda_2)^\lambda - 1}{\lambda} \mbox{ , otherwise} \end{array} \right.

.

The function rboxcox samples Y' from the normal distribution using the function rnorm and backtransform the values according to the equations above to obtain values of Y. If necessary the back-transformation truncates the values such that Y' \geq \frac{1}{\lambda} results in Y = 0 in the original scale. Increasing the value of the mean and/or reducing the variance might help to avoid truncation.

Value

The functions returns the following results:

rboxcox	a vector of random deviates.
dboxcox	a vector of densities.

Author(s)

Paulo Justiniano Ribeiro Jr. [e-mail],
Peter J. Diggle [e-mail].

References

Box, G.E.P. and Cox, D.R.(1964) An analysis of transformations. JRSS B 26:211–246.

See Also

The parameter estimation function is boxcoxfit. Other packages has BoxCox related functions such as boxcox in the package MASS and the function box.cox in the package ‘⁠car⁠’.

Examples

## Simulating data
simul <- rboxcox(100, lambda=0.5, mean=10, sd=2)
##
## Comparing models with different lambdas,
## zero  means and unit variances
curve(dboxcox(x, lambda=-1), 0, 8)
for(lambda in seq(-.5, 1.5, by=0.5))
  curve(dboxcox(x, lambda), 0, 8, add = TRUE)

geoR documentation built on June 8, 2025, 11:03 a.m.