The fifteen density examples used in Marron and Wand (1992)'s
simulation study have been used in quite a few subsequent studies,
can all be written as normal mixtures and are provided here for
convenience and didactical examples of normal mixtures.
Number 16 has been added by Jansen et al.
Marron, S. and Wand, M. (1992)
Exact Mean Integrated Squared Error;
Annals of Statistcs20, 712–736.
For number 16,
Janssen, Marron, Verb..., Sarle (1995) ....
Examples
MW.nm10
plot(MW.nm14)
## These are defined as norMix() calls in ../R/zMarrWand-dens.R
nms <- ls(pat="^MW.nm", "package:nor1mix")
nms <- nms[order(as.numeric(substring(nms,6)))]
for(n in nms) {
cat("\n",n,":\n"); print(get(n, "package:nor1mix"))
}
## Plot all of them:
op <- par(mfrow=c(4,4), mgp = c(1.2, 0.5, 0), tcl = -0.2,
mar = .1 + c(2,2,2,1), oma = c(0,0,3,0))
for(n in nms[-17]) plot(get(n, "package:nor1mix"))
mtext("The Marron-Wand Densities", outer= TRUE, font= 2, cex= 1.6)
## and their Q-Q-plots (not really fast):
prob <- ppoints(N <- 100)
for(n in nms[-17])
qqnorm(qnorMix(prob, get(n, "package:nor1mix")), main = n)
mtext("QQ-plots of Marron-Wand Densities", outer = TRUE,
font = 2, cex = 1.6)
par(op)
## "object" overview:
cbind(sapply(nms, function(n) { o <- get(n)
sprintf("%-18s: K =%2d; rng = [%3.1f, %2.1f]",
attr(o, "name"), nrow(o),
min(o[,"mu"] - 3*sqrt(o[,"sig2"])),
max(o[,"mu"] + 3*sqrt(o[,"sig2"])) )
}))
## Note that Marron-Wand (1992), p.720 give #2 as
MW.nm2
## the parameters of which at first look quite different from
MW.nm2.old
## which has been the definition in the above "Source" Matlab code.
## It's easy to see that mu_{nm2} = -.3 + 1.2 * mu_{paper},
## and correspondigly, s2_{nm2} = 1.2^2 * s2_{paper}
## such that they are "identical" apart from scale and location:
op. <- par(mfrow=2:1, mgp= c(1.2,0.5,0), tcl= -0.2, mar=.1+c(2,2,2,1))
plot(MW.nm2)
plot(MW.nm2.old)
par(op.)