# MarronWand: Marron-Wand Densities as 'norMix' Objects In nor1mix: Normal (1-d) Mixture Models (S3 Classes and Methods)

## Description

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.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ``` MW.nm1 # Gaussian MW.nm2 # Skewed MW.nm2.old # Skewed(old) MW.nm3 # Str Skew MW.nm4 # Kurtotic MW.nm5 # Outlier MW.nm6 # Bimodal MW.nm7 # Separated (bimodal) MW.nm8 # Asymmetric 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

## Source

They have been translated from Steve Marron's Matlab code, now at http://www.unc.edu/depts/stat-or/miscellaneous/marron/parameters/nmpar.m, however for number 2, the Matlab code had `MW.nm2.old`; and I've defined `MW.nm2` as from the Annals paper; see also the last example below.

## References

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) ....

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45``` ```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.) ```

nor1mix documentation built on May 31, 2017, 5:10 a.m.