R: The Box-Cox Transformed Normal Distribution

boxcox {geoR} | R Documentation

## 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' = log(Y) if lambda = 0 , Y' = ((Y ^ lambda) - 1)/lambda otherwise

.

An additional shifting parameter lambda2 can be included in which case the transformation is given by:

Y' = log(Y + lambda2) if lambda = 0 , Y' = (((Y + lambda2) ^ lambda) - 1)/lambda otherwise

.

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' >= -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. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

### 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 `boxcoxfit`, the function `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)

[Package geoR version 1.7-5.2 Index]