cdf_sample <- function(emp_cdf, n=1000) {
  emp_cdf(n)
}


tethai1 <- rnorm(1000, 0, 1)    # eg pdf of prior guess
H1 <- DiscreteDistribution(tethai1)


dp <- function(alpha, H, n=1000) {   
s <- cdf_sample(H,n)            
gam=matrix(0,1,(n+1))
Ginv=matrix(0,1,n)
z=matrix(0,1,n)
p=matrix(0,1,n)
e=rexp((n+1),rate=1)

for(i in 1:(n+1)){
for(j in 1:(i)){
gam[i]=e[j]+gam[i]
}
}

sum1=0
for(i in 1:n){
Ginv[i]=qgamma(1-((gam[i])/(gam[n+1])),shape=(alpha)/n,rate=1)
sum1=Ginv[i]+sum1
}

for(i in 1:n){
p[i]=(Ginv[i])/sum1
}

return(sample(s, 1000, prob=p, replace=TRUE)) 
}


dp_posterior <- function(alpha, H, X) {
m <- length(X)
F_m <- DiscreteDistribution(X)   
F_bar <- m/(m+alpha) * F_m + alpha/(m+alpha) * H
  
   dp(alpha+m, F_bar)
 }

#reapet 5000 
i=1
 w=matrix(0,1,5000)
  while(i<=5000){
 data1 <- rnorm(50,0,1)
 data2 <- rnorm(50,0,1)
 Fpost1 <- dp_posterior(1, H1, data1)
 Fpost2 <- dp_posterior(1, H2, data2)
 F1=ecdf(Fpost1)
 test1=F1(c(Fpost1,Fpost2))
 F2=ecdf(Fpost2)
 test2=F2(c(Fpost1,Fpost2))
 kol=max(abs((test1)-(test2)))
 w[i]=kol
 i=i+1
 }
 
 #compute critical value d_{0}
 q=quantile(T,prob=.975)
 
 #reapet 5000 
i=1
 w=matrix(0,1,5000)
  while(i<=5000){
 data1 <- rnorm(50,0,1)
 data2 <- rnorm(50,1,1)
 Fpost1 <- dp_posterior(1, H1, data1)
 Fpost2 <- dp_posterior(1, H2, data2)
 F1=ecdf(Fpost1)
 test1=F1(c(Fpost1,Fpost2))
 F2=ecdf(Fpost2)
 test2=F2(c(Fpost1,Fpost2))
 kol=max(abs((test1)-(test2)))
 w[i]=kol
 i=i+1
 }

z=0
for(i in 1:5000){
if(w[i]>=q){
z=z+1
}
}
power=z/5000