File:Poissonprozess.png

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R-source code:

set.seed(23092006)
n=30
lambda1=2.4
lambda2=0.6
s1=0
s2=0
for (i in 1:n) {
  s1[i+1]=s1[i]+rexp(n=1, rate=lambda1)
  s2[i+1]=s2[i]+rexp(n=1, rate=lambda2)
}
png(filename="Poissonprozess.png", width=1600, height=1200, pointsize=12)
par(bg="whitesmoke")
p1=stepfun(y=seq(0,n+1),x=s1)
p2=stepfun(y=seq(0,n+1),x=s2)
plot.stepfun(x=p1, do.points=TRUE, col.points="blue", col.hor="blue", verticals=FALSE, lwd=3, xlab="Zeit", ylab="", main="", xlim=c(0,max(s1)) )
plot.stepfun(x=p2, do.points=TRUE, col.points="red", col.hor="red",  verticals=FALSE,  lwd=3, add=TRUE, xlim=c(0,max(s1)) )
title(main="Zwei Pfade von Poisson-Prozessen",cex.main=1.9)
legend(x="bottomright", inset=0.01, cex=1.7, title="Intensitäten", legend=c(expression(lambda[1]==2.4,lambda[2]==0.6)), col=c("blue","red"), lwd=3) 
dev.off()

 

This chart was created with R.