# boxcox

0th

Percentile

##### The Box-Cox Transformed Normal Distribution

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.

Keywords
distribution
##### 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.

##### References

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

The parameter estimation function boxcoxfit, the function boxcox in the package MASS and the function box.cox in the package car.

• rboxcox
• dboxcox
##### Examples
# NOT RUN {
## 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)
# }

Documentation reproduced from package geoR, version 1.8-1, License: GPL (>= 2)

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