Image:Quantile graph.png

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Description

quantiles: from chi-squared disribution (degrees of freedom=3) and the standard-normal distribution. quantiles go up to the corresponding left limit.
Source

created the GNU R, see source below
Date

1 june 2006
Author

Thomas Steiner
Permission
(Reusing this image)

Thomas Steiner put it under the GFDL


GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

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R-source code:

qs=c(0,0.5,0.75,0.9,0.95,0.99)
cs=terrain.colors(length(qs))

qplot<-function(qs,x,pdf,cdf,pfl) {
  plot(x,pdf,type="n",ylim=range(pdf,0)*1.25,xlab="",ylab="")
  for (q in 1:(length(qs)-1)) {
    xd=   x[(cdf>=qs[q])&(cdf<=qs[q+1])]
    yd= pdf[(cdf>=qs[q])&(cdf<=qs[q+1])]
    polygon(c(xd,xd[length(xd)],xd[1]),c(yd,0,0),col=cs[q],border=cs[q])
    lines(c(xd[length(xd)],xd[length(xd)]),c(max(pdf)*1.1-0.01,max(pdf)*1.1+0.01),col=cs[q],lwd=3)
    arrows(xd[length(xd)]-pfl,max(pdf)*1.1,xd[length(xd)],max(pdf)*1.1,lwd=2,length=0.15) 
     text(xd[length(xd)],max(pdf)*1.15,paste("q(",format(qs[q+1]*100),"%)=",format(xd[length(xd)],digits=1,nsmall=1,decimal.mark=","),sep=""),col=cs[q],cex=1.5,adj=c(1,0))
  }
}

png(filename = "Quantile_graph.png", width=1350, height=900, pointsize=12)
par(mfrow=c(2,1),bg="white")

## normalverteilung
x=seq(-0.6,2.3,by=0.0001)
pdf=dnorm(x=x)
cdf=pnorm(q=x)

qplot(qs,x,pdf,cdf,0.35)
title(main="Quantile der Normalverteilung")

## chi-quadrat verteilung
df=3
x=seq(0,11.3,length=10000)
pdf=dchisq(x=x,df=df)
cdf=pchisq(q=x,df=df)

qplot(qs,x,pdf,cdf,1.3)
title(main="Quantile der chi-Quadrat Verteilung")
dev.off()

File history

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Date/TimeDimensionsUserComment
current18:27, 13 September 20071,350×900 (14 KB)Thire (file (white bg))
17:02, 13 September 20071,350×900 (14 KB)Thire (now the file)
10:33, 3 June 20061,500×1,000 (16 KB)Thire ({{Information| |Description = quantiles: from chi-squared disribution (degrees of freedom=3) and the standard-normal distribution. quantiles go up to the corresponding left limit. |Source = created the GNU R, see source below |Date = 1 june 2006 |Author =)
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