MarronWand {nor1mix} | R Documentation |
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.
MW.nm1 # Gaussian MW.nm2 # Skewed MW.nm3 # Str Skew MW.nm4 # Kurtotic MW.nm5 # Outlier MW.nm6 # Biomdal MW.nm7 # Separated (bimodal) MW.nm8 # Aymmettric Bimodal MW.nm9 # Trimodal MW.nm10 # Claw MW.nm11 # Double Claw MW.nm12 # Asymmetric Claw MW.nm13 # Asymm. Double Claw MW.nm14 # Smooth Comb MW.nm15 # Discrete Comb MW.nm16 # Distant Bimodal
Martin Maechler
The first part are translated from Steve Marron's Matlab code at http://www.stat.unc.edu/postscript/papers/marron/parameters/nmpar.m
Marron, S. and Wand, M. (1992) Exact Mean Integrated Squared Error; Annals of Statistcs 20, 712–736.
For number 16,
Janssen, Marron, Verb..., Sarle (1995) ....
MW.nm10 plot(MW.nm14) ## These are defined as norMix() calls in ../R/zMarrWand-dens.R ppos <- which("package:nor1mix" == search()) nms <- ls(pat="^MW.nm", pos = ppos) nms <- nms[order(as.numeric(substring(nms,6)))] for(n in nms) { cat("\n",n,":\n"); print(get(n, pos = ppos)) } ## 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) { plot(get(n, pos = ppos))} 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) { D <- get(n, pos = ppos) qqnorm(qnorMix(D, prob), main = n) } mtext("QQ-plots of Marron-Wand Densities", outer = TRUE, font = 2, cex = 1.6) par(op)