boxcox_plot: Plot Box-Cox transformed density functions

In paulnorthrop/stat1004: stat1004: Introduction to Probability and Statistics at UCL

Description

Box-Cox transforms the input data x and plots a histogram of the transformed data. The Box-Cox transformation parameter is lambda. If the probability density function (pdf) from which the data have arisen is known and the function density_fn is supplied to calculate it then this pdf is also Box-Cox transformed and the resulting transformed pdf is superimposed on the histogram.

Usage

boxcox_plot(x, lambda = 1, density_fn = NULL, breaks = "Sturges",
  main = "", ...)

Arguments

x	A numeric vector of data.
lambda	A numeric scalar. Box-Cox transformation parameter λ.
density_fn	A function to calculate the pdf underlying the input data.
breaks	The argument breaks of hist. Provided to give control of the appearance of histograms.
main	The argument main of hist. Provided to enable a title to the added to the plot.
...	Further arguments to density_fn (if any).

Details

The equation

y = (x ^ λ - 1) / λ.

is a Box-Cox transformation of a variable x to produce a transformed variable variable y. The value of the parameter λ governs the behaviour of the transformation.

See the vignette Chapter 2: Graphs (More Than One Variable) for more details of what the code in Examples below is doing.

Value

Nothing, just the plot.

Examples

# Log-normal distribution --------------------

# X has a log-normal distribution if ln(X) has a normal distribution

# Simulate a sample of size 100 from a log-normal distribution
x <- rlnorm(100)

# Plot the data and the log-normal density function
boxcox_plot(x, density_fn = dlnorm, main = "data and true density function")
# If we want to transform to approximate normality which power should we use?
boxcox_plot(x, density_fn = dlnorm, lambda = 0, main = "after transformation")

# We can use the data to suggest a good value of lambda.
# We need the boxcox() function in the MASS package.
library(MASS)

# Very loosely speaking ...
# In this plot better values of lambda have the largest values.
# "Better" means "transformed data closer to looking like a sample
# from a normal distribution.
# We could choose a nice value of lambda close to the best value.
# The interval is a 95% confidence interval for lambda.
boxcox(x ~ 1)

# exponential distribution --------------------

x2 <- rexp(100)
boxcox_plot(x2 ,density_fn = dexp, main = "data and true density function")

boxcox_plot(x2, density_fn = dexp, lambda = 1 / 3, main = "after transformation")
boxcox(x2 ~ 1)
abline(v = 1/3, col = "red")

# A distribution that I made up --------------------

dpn <- function(x) ifelse(x > 0 & x < 1, 2 * x, 0)
rpn <- function(n = 1) sqrt(runif(n))
x3 <- rpn(100)
boxcox_plot(x3, density_fn = dpn)
boxcox_plot(x3, density_fn = dpn, lambda = 2)

boxcox(x3 ~ 1)
boxcox(x3 ~ 1, lambda = seq(0, 4, 1 / 10))
boxcox_plot(x3, density_fn = dpn, lambda = 1.5)

paulnorthrop/stat1004 documentation built on Nov. 17, 2019, 3:49 a.m.