powTrans: Generalized Box-Cox transformation.
In mlysy/GaussCop: Utilities for the Gaussian Copula Distribution

Description Usage Arguments Details Value Examples

Generalized Box-Cox transformation.

1 2	powTrans(x, lambda = 0, alpha = 0, normalize = FALSE, jacobian = FALSE)

`x`	Vector of quantiles at which to compute the transformation.
`lambda`	Exponent of the transformation. See Details.
`alpha`	Offset of the transformation. See Details.
`normalize`	Logical; if `TRUE` divides by the geometric mean. See Details.
`jacobian`	Logical; if `TRUE` calculates the Jacobian `\|dz / dx\|`, which converts transformed density values back to the original scale.

The Generalized Power or Box-Cox transformation is

z = \begin{array}{rl} ((x + α)^λ - 1) / (λ C^{λ-1}) & λ \neq 0 \ C \log(x + α) & λ = 0, \end{array}

where C is the Geometric mean, i.e., C = exp(mean(log(x + alpha))). Note that C is only calculated if normalize = TRUE.

The vector z of transformed values, and optionally the Jacobian of the inverse transformation. See Details.

# generate data and plot
# apply power transform and superimpose on plot
# finally, superimpose N(0, 1) on plot
n <- 1e5
df <- 5
X <- rchisq(n, df = df)
xdens <- kernelXD(X)
xdens.trans <- kernelXD(powTrans(X))
# plots
curve(dnorm(x), col = "blue", xlim=c(-5, 5), ylim = c(0,0.7)) # true PDF
curve(dXD(x, xDens = xdens), add = TRUE, col = "red") # xDensity PDF
curve(dXD(x, xDens = xdens.trans), add = TRUE, col = "black") # xDensity PDF
legend("topleft", c("N(0, 1", "Chi-Sq(4)", "Power Trans"),
       pch = c(22,22,22,NA), pt.cex = 1.5,
       pt.bg = c("blue", "red", "black"))