remove(list=ls())
set.seed(13)


T<-function(vec,mu){
	sqrt(length(vec))*(mean(vec)-mu)/sd(vec)
}

low<-function(vec,quant){mean(vec)+quant*sd(vec)/sqrt(length(vec))}
up<-function(vec,quant){mean(vec)+quant*sd(vec)/sqrt(length(vec))}

#Number of Bootstrap replications
M<-1000
dat<-read.table("C:/Users/Chris/Documents/Stochastik III/R/lampen.dat")
qqnorm(dat$V2)
qqline(dat$V2,col="red")
hist(dat$V2)
data<-dat$V2
mu<-mean(data)
t.test(data)
n<-length(data)
databoot<-sample(data,size=M*n,replace=TRUE)
databoot<-matrix(databoot,ncol=n)
Tboot<-apply(databoot,1,T,mu=mu)
q1<-quantile(Tboot,probs=c(0.025))
q2<-quantile(Tboot,probs=c(0.975))
low(data,q1)
up(data,q2)
t.test(data)



#####Aufgabe 3#####
KS<-function(vec,mu=0){
	Fn<-ecdf(vec)
	absstand<-abs(Fn(vec)-pnorm(vec,mean=mu))
	max(absstand)
	}

dat<-read.table("C:/Users/Chris/Documents/Stochastik III/R/norm.dat")
dat<-dat$x
n<-length(dat)
M<-5000
t.test(dat)
mu<-mean(dat)
sigma<-sd(dat)
qqnorm(dat)
qqline(dat,col="red")
hist(dat)
ks.test(dat,"pnorm",mean=mean(dat))

KSBasis<-KS((dat-mu)/sigma)
ks.test((dat-mu)/sigma, "pnorm")
bootdat<-rnorm(M*n,mean=mu,sd=sigma)
bootdat<-matrix(bootdat,ncol=n)
means<-apply(bootdat,1,mean)
sds<-apply(bootdat,1,sd)
einser<-rep(1,n)
meansmatrix<-outer(means,einser)
sdmatrix<-outer(sds,einser)
bootdat<-bootdat-meansmatrix
bootdat<-bootdat/sdmatrix
KSstat<-apply(bootdat,1,KS)
length(which(KSstat>KSBasis))/5000


######Erzeuge die Norm Daten#######
hip <- read.table("C:/Users/Chris/Documents/Stochastik III/R/HIP_star.dat",header=TRUE,fill=TRUE)
attach(hip)
filter1 <-  (RA>50 & RA<100 & DE>0 & DE<25)
filter2 <- (pmRA>90 & pmRA<130 & pmDE>-60 & pmDE< -10) 
filter  <-  filter1 & filter2 & (e_Plx<5)
sum(filter)
color <- B.V
boxplot(color~filter,notch=TRUE)

H <- color[filter]
nH <- color[!filter & !is.na(color)]

tlist2 <- NULL
   all <- c(H,nH)
   for(i in 1:5000) {
      s <- sample(2586,92) # choose a sample
      tlist2 <- c(tlist2, t.test(all[s],all[-s],
         var.eq=TRUE)$stat) # add t-stat to list
   }
write.table(tlist2,"C:/Users/Chris/Documents/Stochastik III/R/norm.dat")