## Verdeutlichung des Satzes von Moivre - Laplace ## Bildliche Annäherung plot.binomapproximation <- function(number){ datapoints <- seq(0,number,by=1) result1 <- dbinom(datapoints,number, 0.3) barplot(result1, space=0, names.arg=as.character(datapoints),col = "white",ylim=c(0,dnorm(number*0.3,mean=number*0.3, sd=sqrt(number*0.3*0.7)))) datapoints <- seq(0,number,by=0.1) normalpoints <- dnorm(datapoints, mean=number*0.3, sd=sqrt(number*0.3*0.7)) points(datapoints,normalpoints, type="l", col="blue") } par(mfrow=c(1,3)) n <- 10 plot.binomapproximation(n) n <- 25 plot.binomapproximation(n) n <- 50 plot.binomapproximation(n) ## qq-Plot qqbinplot <- function(number){ datapoints <- rbinom(200,n,0.3) qqnorm(datapoints) abline(n*0.3,sqrt(n*0.3*0.7),col="blue") } par(mfrow=c(2,2)) # normalverteilung datapoints <- rnorm(200) qqnorm(datapoints) abline(0,1,col="blue") n <- 10 qqbinplot(n) n <- 25 qqbinplot(n) n <- 50 qqbinplot(n) ## exponentialverteilung plot.exp <- function(lambda){ datapoints <- seq(0,4*lambda,by=0.01) result1 <- dexp(datapoints,lambda) plot(datapoints,result1, type="l") } sumexp <- function(lambda){ sum(rexp(100,lambda)) } qqexpplot <- function(lambda){ samplesize <- 100 datapoints <- numeric(samplesize) for(i in 1:samplesize) { datapoints[i] <- sumexp(lambda) } qqnorm(datapoints) } par(mfrow=c(1,2)) parameter <- 2 plot.exp(parameter) qqexpplot(parameter)