### 2.2.3 ###

 X <- c(rep(1,17),rep(2,15))
 Y <- c(rep(1,6),rep(2,11),rep(1,2),rep(2,8),rep(3,5))


 mr <- rank(Y)
 w2.mr <- (sort(unique(mr))[2]-min(mr))/(max(mr)-min(mr))
 w2.mr


 F <- ecdf(Y)
 varF <-sort(unique(F(Y)))*(1-sort(unique(F(Y))))
 w2.ad<-(1/sqrt(varF[1]))/(1/sqrt(varF[1])+1/sqrt(varF[2]))
 w2.ad

 source("ptest2s.R")
 set.seed(0)
 B <- 5000
 T <- ptest2s(Y,X,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs


 Y.mr <- Y
 Y.mr[Y.mr==1] <- 0
 Y.mr[Y.mr==2] <- w2.mr
 Y.mr[Y.mr==3] <- 1
 set.seed(0)
 T <- ptest2s(Y.mr,X,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs


 Y.ad <- Y.mr
 Y.ad[Y.ad==w2.mr] <- w2.ad
 set.seed(0)
 T <- ptest2s(Y.ad,X,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs



 source("Tmax.R")
 set.seed(0)
 T <- ptest2s(Y,X,B,"Tmax")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs


### 2.2.5 ###


 X <- c(rep(1,17),rep(2,15))
 YI <- c(rep(1,5),rep(2,11),3,rep(1,3),rep(2,8),rep(3,4))
 YII <- c(rep(2,16),rep(3,1),rep(1,8),rep(2,3),rep(3,4))

 source("LRT.R")
 LRT(YI[X==1],YI[X==2])

 LRT(YII[X==1],YII[X==2])

 source("DChisq.R")
 DChisq(YI,X)

 DChisq(YII,X)

 source("studT.R")
 studT(YI[X==1],YI[X==2])

 studT(YI[X==1],YI[X==2])


 source("Tmax.R")
 Tmax(YI[X==1],YI[X==2])

 Tmax(YII[X==1],YII[X==2])



### 2.3.1 ###


 X <- c(rep(1,17114),rep(2,14502),rep(3,793),rep(4,127),rep(5,38))
 Y<-c(rep(0,17066),rep(1,48),rep(0,14464),rep(1,38),rep(0,788),rep(1,5),rep(0,126),rep(1,1),rep(0,37),rep(1,1))

 source("ptest2s.R")
 set.seed(0)
 B <- 1000
 T <- ptest2s(X,Y,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs

 set.seed(0)
 X.d <- c(rep(0,17114),rep(.5,14502),rep(1.5,793),rep(4,127),rep(7,38))
 T <- ptest2s(X.d,Y,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs


 set.seed(0)
 X.mr <- rank(X)
 T <- ptest2s(X.mr,Y,B,"Student")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs


 source("Tmax.R")
 set.seed(0)
 T <- ptest2s(X,Y,B,"Tmax")
 p.obs <- sum(T[-1]>=T[1])/(B-1)
 p.obs






 X <- c(rep(1,13),rep(2,12),rep(3,13),rep(4,14))
 Y <- c(rep(0,4),rep(1,9),rep(0,8),rep(1,4),rep(0,7),rep(1,6),rep(0,1),rep(1,13))

 source("ptestRs.R")
 set.seed(0)
 B <- 5000
 T123 <- ptestRs(Y,X,B,combi="max")
 p.obs <- sum(T123[-1]>=T123[1])/(B-1)
 p.obs

 T12 <- ptestRs(Y[X!=4],X[X!=4],B,combi="max")
 sum(T12[-1]>=T12[1])/(B-1)

 T13 <- ptestRs(Y[X!=3],X[X!=3],B,combi="max")
 sum(T13[-1]>=T13[1])/(B-1)

 T23 <- ptestRs(Y[X!=2],X[X!=2],B,combi="max")
 sum(T23[-1]>=T23[1])/(B-1)


 T1 <- ptest2s(Y[X!=3&X!=4],X[X!=3&X!=4],B,"Student")
 sum(T1[-1]>=T1[1])/(B-1)

 T2 <- ptest2s(Y[X!=2&X!=4],X[X!=2&X!=4],B,"Student")
 sum(T2[-1]>=T2[1])/(B-1)

 T3 <- ptest2s(Y[X!=2&X!=3],X[X!=2&X!=3],B,"Student")
 sum(T3[-1]>=T3[1])/(B-1)