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# Experiment zur Approximation von Binomial- durch Poisson-Verteilung
source(file="http://www.wiwi.uni-bielefeld.de/~wolf/software/R-wtools/slider/slider.R")

binom.to.poisson<-function(){
  refresh.code<-function(...){
  # Vorbereitung
    n<-slider(no=1); lambda<-slider(no=2); x.0<-slider(no=3)
    if(lambda>n)n<-slider(set.no.value=c(1,ceiling(lambda)))
 # Berechnung
    p<-lambda/n
    x<-max(0,round(n*p-3*lambda^0.5)):round(n*p+3*lambda^0.5);
    f.poisson<-dpois(x,lambda); f.binom<-dbinom(x,n,p)
    if(x.0<x[1])x.0<-slider(set.no.value=c(3,x[1]))
    if(x.0>max(x))x.0<-slider(set.no.value=c(3,max(x)))
  # Plot
    nice<-function(x,st=4)paste(floor(x),".",substring(round(1E4*(1+x%%1)),2,1+st),sep="")
    par(mfrow=c(3,1))
    plot(x,f.poisson,type="h",bty="l",main=paste("poisson: lambda=",nice(lambda,1),sep=""))
    abline(v=x.0, col="red", lty=2)
    ymax<-par()$usr[4]; xdel<-diff(par()$usr[1:2])
    if(lambda>5){pos<-4;xt<-par()$usr[1]+xdel/30}else{pos<-2;xt<-par()$usr[2]-xdel/6}
    text(xt,ymax*0.9,pos=pos,paste("P(X= ",x.0,")=",nice(dpois(x.0,lambda)),sep=""))
    text(xt,ymax*0.8,pos=pos,paste("P(X<=",x.0,")=",nice(ppois(x.0,lambda)),sep=""))
    text(xt,ymax*0.7,pos=pos,paste("P(X> ",x.0,")=",nice(1-ppois(x.0,lambda)),sep=""))
    plot(x,f.binom,type="h",bty="l",ylim=c(0,ymax),
         main=paste("binomial: n=",n,",p=",nice(p),sep=""))
    plot(x,f.poisson-f.binom,type="h",bty="l",main="Unterschiede")
    abline(h=0)
    par(mfrow=c(1,1))
  }
  slider(refresh.code,
       c("n: Anzahl Experimente",
          "lambda: E(X) aus Poisson","x.0: spezielle Stelle"),
       c(1,1,1),c(10000,99,99),c(1,.1,1),c(100,10,5)  )
}

binom.to.poisson()
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