****The empirical distribution function
**Uniform distribution


n<-100
data<-sort(runif(n))
x.points<-(1:1000)/1000
Fn<- (1:n)/n
par(col="black")
plot(x.points,punif(x.points),type="l",ylim=c(0,1),xlim=range(x.points))
par(new=TRUE, col="red")
plot(data,Fn,type="s",ylim=c(0,1),xlim=range(x.points))


**Normal distr.
n<-100
data<-sort(rnorm(n))
x.points<-(-1000:1000)/100
Fn<- (1:n)/n
par(col="black")
plot(x.points,pnorm(x.points),type="l",ylim=c(0,1),xlim=range(x.points))
par(new=TRUE, col="red")
plot(data,Fn,type="s",ylim=c(0,1),xlim=range(x.points))


**Exponential distribution
n<-30
data<-sort(rexp(n))
x.points<-(1:1000)/100
Fn<- (1:n)/n
par(col="black")
plot(x.points,pexp(x.points),type="l",ylim=c(0,1),xlim=range(x.points))
par(new=TRUE, col="red")
plot(data,Fn,type="s",ylim=c(0,1),xlim=range(x.points))



****Donskers theorem


**Uniform distr

n<-100000
data<-sort(runif(n))
x.points<-(1:1000)/1000
Fn<- (1:n)/n
par(col="black")
plot(data,sqrt(n)*(Fn-punif(data)),type="l")

**Exponential distribution
n<-1000
data<-sort(rexp(n))
Fn<- (1:n)/n
par(col="black")
plot(data,sqrt(n)*(Fn-pexp(data)),type="l")
***transformd to see the Brownian bridge
plot(pexp(data),sqrt(n)*(Fn-pexp(data)),type="l")

**Normal distribution
n<-1000
data<-sort(rnorm(n))
Fn<- (1:n)/n
par(col="black")
plot(data,sqrt(n)*(Fn-pnorm(data)),type="l")
***transformd to see the Brownian bridge
plot(pnorm(data),sqrt(n)*(Fn-pnorm(data)),type="l")