gc4XD: Construct an 'xDensity' representation of a combined...
In mlysy/GaussCop: Utilities for the Gaussian Copula Distribution

Description Usage Arguments Details Value See Also Examples

Construct an xDensity representation of a combined Box-Cox/Gram-Charlier density approximation.

1 2	gc4XD(x, lambda = NULL, alpha = 0, cmom = NULL, trim = 0.01, n = 512, from, to, mean, sd, ...)

`x`	Vector of random samples from density to approximate.
`lambda`	Exponent of Box-Cox transform. If `NULL` it is estimated from `x`. See Details.
`alpha`	Offset of the Box-Cox transform. Default is no offset. See Details.
`cmom`	Optional vector of first 4 central moments of `x`. If `NULL` these are estimated from `x`.
`trim`	Scalar between 0 and 1; removes the `trim` fraction of extreme values from `x` for estimation of `lambda` and `cmom`, which are very sensitive to outliers. `trim = FALSE` does not trim any values.
`n, from, to`	Specifies a grid of values on which to evaluate the density (see `density`).
`mean, sd`	Optional mean and standard deviation for `xDensity` representation.
`...`	Additional parameters to Box-Cox fitting function `powFit`.

x is first standardized to z = x/sd(x) - min(x/sd(x), from) + 1, before the Box-Cox transform is applied.

For details on the Box-Cox transformation and Gram-Charlier approximation, see powFit and dgc4 respectively.

An xDensity object.

powFit, dgc4, xDensity.

# xDensity approximation to a noncentral-t distribution

# true parameters
lambda <- rnorm(1) # noncentrality parameter
nu <- runif(1, 4, 6) # degrees of freedom

# simulate data (note the small sample size)
x <- rt(500, df = nu, ncp = lambda)

# xDensity approximation
xDensK <- kernelXD(x) # kernel smoothing
xDensG <- gc4XD(x) # gc4 approximation

# true vs approximate PDFs
xlim <- qt(c(.005, .995), df = nu, ncp = lambda) # range for plot
curve(dt(x, df = nu, ncp = lambda),
      from = xlim[1], to = xlim[2], ylab = "Density")
curve(dXD(x, xDens = xDensK), add = TRUE, col = "red")
curve(dXD(x, xDens = xDensG), add = TRUE, col = "blue")
legend("topleft", legend = c("True PDF", "xDensity: kernel", "xDensity: gc4"),
       fill = c("black", "red", "blue"))