R/zMarrWand-dens.R

In nor1mix: Normal aka Gaussian 1-d Mixture Models

#### {filename starting with 'z' : must come after other the Normix() defining code}

### The first part of this is from  Steve Marron,
### from his Matlab code
###         ftp://ftp.stat.unc.edu/pub/papers/marron/parameters/nmpar.m
##
##    For generating Normal mixture parameters,
##      of the 15 Normal Mixture densities
##      from Marron and Wand (1992),
##      plus number 16 from Janssen, et. al.

MW.nm1 <- norMix(name = "#1 Gaussian", mu = 0, sigma = 1, w = 1)

## This is from the above Matlab code:
MW.nm2.old <- norMix(name = "#2 Skewed (old)",
		     mu	  = c(-.3, .3, 1),
		     sigma= c(1.2, .8, 2/3),
		     w	  = c(.2, .2, .6))
## Note that Marron-Wand (1992), p.720	give #2 as
MW.nm2 <- norMix(name = "#2 Skewed",
		  mu   = c(0, .5, 13/12),
		  sigma= c(1, (2/3), (5/9)),
		  w    = c(.2, .2, .6))
## which at first looks quite different
## but it's easy to see mu_{nm2.old}  = -.3 + 1.2 * mu_{paper},
## and correspondigly,  s2_{nm2.old } = 1.2^2 * s2_{paper}
## such that they are "identical" apart from scale and location

sig <- (2/3)^(0:7)
MW.nm3 <- norMix(name = "#3 Str Skew",
		 mu   = 3 * (sig - 1),
		 sigma = sig,
		 w    = rep(1,8) / 8)

MW.nm4 <- norMix(name = "#4 Kurtotic",
		 mu   = c(0, 0),
		 sigma= c(1 , .1),
		 w    = c(2/3, 1/3))


MW.nm5 <- norMix(name = "#5 Outlier",
		 mu   = c(0, 0),
		 sigma= c(1, .1),
		 w    = c(.1, .9))

MW.nm6 <- norMix(name = "#6 Bimodal",
		 mu   = c(-1, 1),
		 sigma= c(2/3, 2/3),
		 w = c(.5, .5))

MW.nm7 <- norMix(name = "#7 Separated",
		 mu  = c(-1.5, 1.5),
		 sigma= c(1/2, 1/2),
		 w = c(.5, .5))

MW.nm8 <- norMix(name = "#8 Asym Bim",
		 mu   = c(0, 1.5),
		 sigma= c(1, 1/3),
		 w = c(.75, .25))

MW.nm9 <- norMix(name = "#9 Trimodal",
		 mu   = c(-1.2, 1.2, 0),
		 sigma= c(3/5, 3/5, 1/4),
		 w = c(.45, .45, .1))

MW.nm10 <- norMix(name = "#10 Claw",
		  mu = c(0, seq(-1,1, by = .5)),
		  sigma= c(1, rep(0.1, 5)),
		  w = c(.5, rep(.1, 5)))


MW.nm11 <- norMix(name = "#11 Doub Claw",
		  mu = c(-1, 1,seq(-1.5,1.5, by = .5)),
		  sigma= c(2/3, 2/3, rep(.01, 7)),
		  w = c(.98*c(.5, .5), .02*rep(1,7)/7))


mu <- .5 + -2:2
sig <- c(0.4, 0.2, 0.1, 0.05, 0.025)
w <- sig
MW.nm12 <- norMix(name = "#12 Asym Claw",
		  mu   = c(0, mu),
		  sigma= c(1, sig),
		  w    = c(1, w/sum(w))/2)


mu <- c(-1.5, -1, -.5)
sig <- rep(.01, 3)
w <- rep(1/3,3)
MW.nm13 <- norMix(name = "#13 As Do Claw",
		  mu   = c(  -1,  1,    mu,  mu + 2),
		  sigma= c(2/3, 2/3, sig, 7*sig),
		  w    = c(.46, .46, .01*w,  .07*w))


n <- 6
sig <- 2^(0:(1-n)) # =  2^{1-j} , j=1,2,..,n
il <- -3
##- ir <- 3
##- mu <- numeric(n)
##- for(i in 2:n) {
##-   mu[i] <- ir + 3 * sig[i] #-- mu_i  = ir_{i-1} + 3 s_i  = (ir_{i-1}+ir_i)/2
##-   ir    <- ir + 6 * sig[i] #-- ir_i  = -3 + sum_{j=1}^i (6 * s_j)
##- }
irv <- -3 + 6*cumsum(sig)
mu <- c(0, (irv[-1] + irv[-n])/2)
di <- irv[n] - il
MW.nm14 <- norMix(name = "#14 Smoo Comb",
		  mu   = 6 * ((mu - il) / di) - 3,
		  sigma= 6 * sig / di,
		  w    = sig / sum(sig))


mu  <- c(0, 6, 12, 15.5, 16.5, 17.5)
sig <- c(1, 1,  1,  1/6,  1/6,  1/6)
il <- -3 ; ir <- 18
di <- ir - il
MW.nm15 <- norMix(name = "#15 Disc Comb",
		  mu   = 6 * ((mu - il) / di) - 3,
		  sigma= 6 * sig / di,
		  w    = sig / sum(sig))

MW.nm16 <- norMix(name = "#16 Dist Bim",
		  mu   = c(-2.5, 2.5),
		  sigma= c( 1/6, 1/6),
		  w    = c(0.5,  0.5))

## clean up:
rm(n, mu, sig, w, il,ir,irv,di)