Skip to content

mixture normal distributions

3 messages · aleid2001@yahoo.com, Martin Maechler

aleid2001@yahoo.com
# 
Dear R helper,

I mange to transform uniform sequences to mixture
normal distributions using the following cods:
w = c(0.25,0.75), name = NULL, long.name = FALSE)
But somtimes if i use ,e.g, 23 or 11 instead of 29 it
will give me the following error.
w = c(0.25,0.75), name = NULL, long.name = FALSE)
Error in uniroot(function(l) pnorMix(obj, l) - pp[i],
interval = rq) : 
        f() values at end points not of opposite sign


I am seeking help how to avoid this error.

Many thanks for your help in advance.

My E-mail is aleid2001 at yahoo.com

Al-Eid

The university of Manchester.
Martin Maechler
# 
you forgot to mention the important fact that you are working
with package  "nor1mix"  (of which I am the maintainer which you
could have seen from   library(help = nor1mix)  or 
packageDescription("nor1mix")
This looks like you want to generate pseudo-random values from
the mixture distribution.

However by the slowest most possible way:  qnorMix() is really
slow because it calls uniroot() for each value.

rnorMix() will generate random values distributed according to
the normal mixture very very efficiently (particularly compared
to using qnorMix()).

But indeed, you have detected a bug in qnorMix() 
(that happens pretty rarely).  Indeed your example also shows
that the algorithm can be much improved in some cases.

The next verion of nor1mix  should  contain a more "robust"
qnorMix() function.
Martin Maechler
# 
>>> Dear R helper, I mange to transform uniform sequences to
    >>> mixture normal distributions using the following cods:

    Martin> you forgot to mention the important fact that you
    Martin> are working with package "nor1mix" (of which I am
    Martin> the maintainer which you could have seen from
    Martin> library(help = nor1mix) or
    Martin> packageDescription("nor1mix")


    >>> > K<-50000 > prime<-c(29) , where 29 is prim number >
    >>> UN<-seq(1:K)%*%t(sqrt(prime)) > U1<-UN-as.integer(UN) >
    >>> e<-norMix(mu=c(-0.825,0.275), sig2 = c(0.773,0.773), w =
    >>> c(0.25,0.75), name = NULL, long.name = FALSE) >
    >>> U<-matrix(qnorMix(e,U1),K,1),

    Martin> This looks like you want to generate pseudo-random
    Martin> values from the mixture distribution.

    Martin> However by the slowest most possible way: qnorMix()
    Martin> is really slow because it calls uniroot() for each
    Martin> value.

    Martin> rnorMix() will generate random values distributed
    Martin> according to the normal mixture very very
    Martin> efficiently (particularly compared to using
    Martin> qnorMix()).

    Martin> But indeed, you have detected a bug in qnorMix()
    Martin> (that happens pretty rarely).  Indeed your example
    Martin> also shows that the algorithm can be much improved
    Martin> in some cases.

    Martin> The next verion of nor1mix should contain a more
    Martin> "robust" qnorMix() function.

in the mean time, you can use the following which already fixes
the problem you found :

qnorMix <- function(obj, p)
{
  if (!is.norMix(obj))
     stop("'obj' must be a 'Normal Mixture' object!")
  mu <- obj[, "mu"]
  sd <- sqrt(obj[, "sig2"])
  k <- nrow(obj)# = #{components}
  if(k == 1) # one component
      return(qnorm(p, mu, sd))

  ## else

  ## vectorize in `p' :
  r <- p
  left  <- p <= 0 ; r[left] <- -Inf
  right <- p >= 1 ; r[right] <- Inf
  imid <- which(mid <- !left & !right) # 0 < p < 1
  ## p[] increasing for easier root finding start:
  p <- sort(p[mid], index.return = TRUE)
  ip <- imid[p$ix]
  pp <- p$x
  for(i in seq(along=pp)) {
      rq <- range(qnorm(pp[i], mu, sd))
      ## since pp[] is increasing, we can start from last 'root':
      if(i > 1) rq[1] <- root
      ## make sure, 'lower' is such that f(lower) < 0 :
      delta.r <- 0.01*abs(rq[1])
      ff <- function(l) pnorMix(obj,l) - pp[i]
      while(ff(rq[1]) > 0) rq[1] <- rq[1] - delta.r

      root <- uniroot(ff, interval = rq)$root
      r[ip[i]] <- root
  }
  r
}


I hope this helps you.




    >>> But somtimes if i use ,e.g, 23 or 11 instead of 29 it
    >>> will give me the following error.
    >>> 
    >>> > K<-30000 > prime<-c(23) >
    >>> UN<-seq(1:K)%*%t(sqrt(prime)) > U1<-UN-as.integer(UN) >
    >>> e<-norMix(mu=c(-0.825,0.275), sig2 = c(0.773,0.773), w =
    >>> c(0.25,0.75), name = NULL, long.name = FALSE) >
    >>> U<-matrix(qnorMix(e,U1),K,1) Error in
    >>> uniroot(function(l) pnorMix(obj, l) - pp[i], interval =
    >>> rq) : f() values at end points not of opposite sign
    >>> 
    >>> 
    >>> I am seeking help how to avoid this error.
    >>> 
    >>> Many thanks for your help in advance.
    >>> 
    >>> My E-mail is aleid2001 at yahoo.com
    >>> 
    >>> Al-Eid
    >>> 
    >>> The university of Manchester.

    Martin> ______________________________________________
    Martin> R-help at stat.math.ethz.ch mailing list
    Martin> https://stat.ethz.ch/mailman/listinfo/r-help PLEASE
    Martin> do read the posting guide!
    Martin> http://www.R-project.org/posting-guide.html