library(nleqslv)
FindRoot = function(x,gamma1,gamma2,alpha) {
return(pnorm(x-gamma2)-exp(2*gamma2*x)*pnorm(-x-gamma2)-1+alpha)
}
MAX<-25
max<-500
Qn1<-rep(0,max)
Times1<-rep(0,max)
n<-100
mu<--0.5
c<-0.5
d_0<-1
Z_alpha<-nleqslv(1, FindRoot, control=list(btol=.000001),jacobian=TRUE,method="Newton",gamma1=gamma1,gamma2=-d_0,alpha= 0.05)$x
for(k in 1:max){
Tn1<-rep(0,MAX)
Tn2<-rep(0,MAX)
Tn3<-rep(0,MAX)
Tn4<-rep(0,MAX)
for(j in 1:MAX){ if(j<=1){h=rnorm(1,0,1)}else{h=-1}
X<-rnorm(n,mu,1)
hatsigma1<-sd(X)
x<-c-X
if(((sum(Tn2[1:j]+Tn4[1:j]))/((MAX))+sum(Tn1[1:j]+Tn3[1:j])/(sqrt(MAX)*sqrt((hatsigma^2/n))))<=0 & h<0){
#xx<-sample(x,n,replace=TRUE)
#yy<-sample(y,n,replace=TRUE)
#hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn1[j]<-mean(x)-d_0
Tn2[j]<-mean(x)
}else{
# hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn3[j]<-d_0-mean(x)
Tn4[j]<--mean(x)}
}
Qn1[k]<-sum(Tn2+Tn4)/(MAX)+sum(Tn1+Tn3)/(sqrt(MAX)*sqrt((hatsigma^2/n)))
Times1[k]<-(abs(Qn1[k])>Z_alpha)+0
}
densityf<-function(y,alpha,c){
exp(-(y^2-2*alpha*(abs(y-c)-abs(c))+alpha^2)/2)/sqrt(2*pi)-
alpha*exp(2*alpha*abs(y-c))*(1-pnorm(abs(c)+abs(y-c)+alpha,0,1))
}
YY<-seq(-5,5,length=100)
Alpha<--d_0
res<-array(0,dim=c(length(YY),length(Alpha)))
for(j in 1:length(YY)){
for(k in 1:length(Alpha))
res[j,k]<-densityf(YY[j],Alpha[k],0)
}
plot(YY,res,type="l",ylab="density",xlab="",col="blue",ylim = c(0,1.1))
lines(density(Qn1),ylab="density",col="red",xlab="")
mean(Times1)
library(nleqslv)
FindRoot = function(x,gamma1,gamma2,alpha) {
return(pnorm(x-gamma2)-exp(2*gamma2*x)*pnorm(-x-gamma2)-1+alpha)
}
MAX<-25
max<-500
Qn1<-rep(0,max)
Times1<-rep(0,max)
n<-100
mu<--0.5
c<-0.5
d_0<-1
Z_alpha<-nleqslv(1, FindRoot, control=list(btol=.000001),jacobian=TRUE,method="Newton",gamma1=gamma1,gamma2=-d_0,alpha= 0.05)$x
for(k in 1:max){
Tn1<-rep(0,MAX)
Tn2<-rep(0,MAX)
Tn3<-rep(0,MAX)
Tn4<-rep(0,MAX)
for(j in 1:MAX){ if(j<=1){h=rnorm(1,0,1)}else{h=-1}
X<-rnorm(n,mu,1)
hatsigma1<-sd(X)
x<-c-X
if(((sum(Tn2[1:j]+Tn4[1:j]))/((MAX))+sum(Tn1[1:j]+Tn3[1:j])/(sqrt(MAX)*sqrt((hatsigma^2/n))))<=0 & h<0){
#xx<-sample(x,n,replace=TRUE)
#yy<-sample(y,n,replace=TRUE)
#hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn1[j]<-mean(x)-d_0
Tn2[j]<-mean(x)
}else{
# hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn3[j]<-d_0-mean(x)
Tn4[j]<--mean(x)}
}
Qn1[k]<-sum(Tn2+Tn4)/(MAX)+sum(Tn1+Tn3)/(sqrt(MAX)*sqrt((hatsigma^2/n)))
Times1[k]<-(abs(Qn1[k])>Z_alpha)+0
}
densityf<-function(y,alpha,c){
exp(-(y^2-2*alpha*(abs(y-c)-abs(c))+alpha^2)/2)/sqrt(2*pi)-
alpha*exp(2*alpha*abs(y-c))*(1-pnorm(abs(c)+abs(y-c)+alpha,0,1))
}
YY<-seq(-5,5,length=100)
Alpha<--d_0
res<-array(0,dim=c(length(YY),length(Alpha)))
for(j in 1:length(YY)){
for(k in 1:length(Alpha))
res[j,k]<-densityf(YY[j],Alpha[k],0)
}
plot(YY,res,type="l",ylab="density",xlab="",col="blue",ylim = c(0,1.1))
lines(density(Qn1),ylab="density",col="red",xlab="")
mean(Times1)
############################################################################
library(nleqslv)
FindRoot = function(x,gamma1,gamma2,alpha) {
return(pnorm(x-gamma2)-exp(2*gamma2*x)*pnorm(-x-gamma2)-1+alpha)
}
MAX<-25
max<-500
Qn1<-rep(0,max)
Times1<-rep(0,max)
n<-100
mu<--0.5
c<-0.5
d_0<-1.1
Z_alpha<-nleqslv(1, FindRoot, control=list(btol=.000001),jacobian=TRUE,method="Newton",gamma1=gamma1,gamma2=-d_0,alpha= 0.05)$x
for(k in 1:max){
Tn1<-rep(0,MAX)
Tn2<-rep(0,MAX)
Tn3<-rep(0,MAX)
Tn4<-rep(0,MAX)
for(j in 1:MAX){
X<-rnorm(n,mu,1)
hatsigma1<-sd(X)
x<-c-X
if(j<=1){h=rnorm(1,0,1)}else{h=-1}
if(((sum(Tn2[1:j]+Tn4[1:j]))/((MAX))+sum(Tn1[1:j]+Tn3[1:j])/(sqrt(MAX)*sqrt((hatsigma^2/n))))<=0& h<0){
#xx<-sample(x,n,replace=TRUE)
#yy<-sample(y,n,replace=TRUE)
#hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn1[j]<-mean(x)-d_0
Tn2[j]<-mean(x)
}else{
# hatsigma1<-sd(xx)
#  hatsigma2<-sd(yy)
Tn3[j]<-d_0-mean(x)
Tn4[j]<--mean(x)}
}
Qn1[k]<-sum(Tn2+Tn4)/(MAX)+sum(Tn1+Tn3)/(sqrt(MAX)*sqrt((hatsigma^2/n)))
Times1[k]<-(abs(Qn1[k])>Z_alpha)+0
}
densityf<-function(y,alpha,c){
exp(-(y^2-2*alpha*(abs(y-c)-abs(c))+alpha^2)/2)/sqrt(2*pi)-
alpha*exp(2*alpha*abs(y-c))*(1-pnorm(abs(c)+abs(y-c)+alpha,0,1))
}
YY<-seq(-5,5,length=100)
Alpha<--d_0
res<-array(0,dim=c(length(YY),length(Alpha)))
for(j in 1:length(YY)){
for(k in 1:length(Alpha))
res[j,k]<-densityf(YY[j],Alpha[k],0)
}
plot(YY,res,type="l",ylab="density",xlab="",col="blue",ylim = c(0,1.5),xlim = c(-7,7))
lines(density(Qn1),ylab="density",col="red",xlab="")
mean(Times1)
