tukeyPsi1 {robustbase} | R Documentation |
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) ~= x around 0.
tukeyPsi1(x, cc, deriv = 0)
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. |
a numeric vector of the same length as x
.
tukeyPsi1(x, d)
and tukeyChi(x, d+1)
and are just
re-scaled versions of each other (for d in -1:1
).
We use the name ‘tukeyPsi1’, because tukeyPsi
is
reserved for a future “Psi Function” class object, see
psiFunc
.
Matias Salibian-Barrera, Martin Maechler and Andreas Ruckstuhl
lmrob
and tukeyChi
; further
anova.lmrob
which needs the deriv = -1
.
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)