robustbase (version 0.5-0-1)

tukeyPsi1: Tukey's Bi-square Score (Psi) Function and Derivative

Description

Compute Tukey's bi-square score (psi) function, its first derivative or it's integral/principal function. This is scaled such that $\psi'(0) = 1$, i.e., $\psi(x) \approx x$ around 0.

Usage

tukeyPsi1(x, cc, deriv = 0)

Arguments

x

numeric vector.

cc

tuning constant

deriv

integer in ${-1,0,1}$ specifying the order of the derivative; the default, deriv = 0 computes the psi-function.

Value

• a numeric vector of the same length as x.

See Also

lmrob and tukeyChi; further anova.lmrob which needs the deriv = -1.

Examples

op <- par(mfrow = c(3,1), oma = c(0,0, 2, 0),
          mgp = c(1.5, 0.6, 0), mar= .1+c(3,4,1,1))
x <- seq(-5, 5, length = 201)
cc <- 4.69 # as set by default in lmrob.control()
plot. <- function(...) { plot(..., asp = 1); abline(h=0,v=0, col="gray", lty=3)}
plot.(x, tukeyPsi1(x, cc), type = "l", col = 2)
abline(0:1, lty = 3, col = "light blue")
plot.(x, tukeyPsi1(x, cc, deriv = -1), type = "l", col = 2)
plot.(x, tukeyPsi1(x, cc, deriv =  1), type = "l", col = 2); abline(h=1,lty=3)mtext(sprintf("tukeyPsi1(x, c = %g, deriv),  deriv = 0, -1, 1", cc),
      outer = TRUE, font = par("font.main"), cex = par("cex.main"))
par(op)