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#' GPQW
#'
#' A method based on generalized pivotal quantity with order statistics(also see \code{\link{GPQH}}) to construct the simultaneous confidence intervals for
#' Ratios of Means of Log-normal Populations with Zeros.
#'
#' More information about GPQW, you can read the paper: Simultaneous Confidence Intervals for Ratios of Means of Log-normal Populations with Zeros.
#'
#' @name GPQW
#' @aliases GPQW
#' @usage GPQW(n,p,mu,sigma,N,C2=rbind(c(-1,1,0),c(-1,0,1),c(0,-1,1)),alpha=0.05)
#'
#' @param n The sample size of the mixture distributions,must be an integer vector.
#' @param p The zero probability of the mixture distribution,it has the same length to the \strong{n} params.
#' @param mu The mean of the non-zero samples,which after log-transformation.
#' @param sigma The variance of the non-zero samples,which after log-transformation.
#' @param N The number of independent generated data sets.
#' @param C2 Matrix C,You can refer to the paper of Xu et al. for specific forms.
#' @param alpha The confidence level,it always set \emph{alpha=0.5}
#'
#' @return The method will return the Simultaneous Confidence Intervals(SCIs) and the time consuming
#'
#' @author Jing Xu, Xinmin Li, Hua Liang
#'
#' @examples
#'
#'
#'alpha <- 0.05
#'
#'p <- c(0.1,0.15,0.1)
#'n <- c(30,15,50)
#'mu <- c(0,0,0)
#'sigma <- c(1,1,1)
#'N <- 100
#'GPQW(n,p,mu,sigma,N)
#'
#'\dontrun{
#'p <- c(0.1,0.15,0.1,0.6)
#'n <- c(30,15,10,50)
#'mu <- c(0,0,0,0)
#'sigma <- c(1,1,1,2)
#'C2 <- rbind(c(-1,1,0,0),c(-1,0,1,0),c(-1,0,0,1),c(0,-1,1,0),c(0,-1,0,1),c(0,0,-1,1))
#'
#'N <- 1000;
#'GPQW(n,p,mu,sigma,N,C2 = C2)
#'
#'}
#'
#' @export GPQW
GPQW0<-function(n,p,mu,sigma,N,C2=rbind(c(-1,1,0),c(-1,0,1),c(0,-1,1)),alpha=0.05){
t1<-Sys.time()
result<-list()
r = r1 = r2 = matrix(0,dim(C2)[1],N)
for(i in 1:length(n)){
assign(paste0('n',i,'0'),rbinom(1,n[i],p[i]))
assign(paste0('n',i,'1'),n[i]-get(paste0('n',i,'0')))
assign(paste0('y',i,'bar'),rnorm(1,mu[i],(sigma[i]/sqrt(sqrt(get(paste0('n',i,'1')))))))
assign(paste0('s',i,'sq'),(sigma[i])^2*rchisq(1,df=(get(paste0('n',i,'1'))-1),ncp=0))
assign(paste0('Z',i),rnorm(N,0,1))
assign(paste0('U',i),rchisq(N,df=(get(paste0('n',i,'1'))-1),ncp=0))
assign(paste0('Z',i,'W'),rnorm(N,0,1))
#assign(paste0('TPW',i),numeric(N))
#assign(paste0('TW',i),numeric(N))
}
for(k in 1:N){
tempTW <- list()
for(i in 1:length(n)){
assign(paste0('TPW',i,'[',k,']'),
(get(paste0('n',i,'0')) + 0.5 * (get(paste0('Z',i,'W'))[k])^2)/(n[i] + (get(paste0('Z',i,'W'))[k])^2)-
(get(paste0('Z',i,'W'))[k] * sqrt(get(paste0('n',i,'0'))*(1 - get(paste0('n',i,'0'))/n[i]) +
(get(paste0('Z',i,'W'))[k])^2/4))/(n[i] + (get(paste0('Z',i,'W'))[k])^2)
)
#TPW1[k]<-(n10+0.5*(Z1W[k])^2)/(n1+(Z1W[k])^2)-(Z1W[k]*sqrt(n10*(1-n10/n1)+(Z1W[k])^2/4))/(n1+(Z1W[k])^2);
assign(paste0('TW',i,'[',k,']'),log(1-get(paste0('TPW',i,'[',k,']')))+
(get(paste0('y',i,'bar'))-get(paste0('Z',i))[k]*sqrt(get(paste0('s',1,'sq')))/
(sqrt(get(paste0('n',i,'1'))*get(paste0('U',i))[k]))+
get(paste0('s',1,'sq'))/(2*get(paste0('U',i))[k]))
)
#TW1[k]<-log(1-TPW1[k])+(y1bar-Z1[k]*sqrt(s1sq)/(sqrt(n11*U1[k]))+s1sq/(2*U1[k]));
tempTW[[i]] <- get(paste0('TW',i,'[',k,']'))
}
r[,k] <- C2 %*% unlist(tempTW)
}
for(i in 1: dim(C2)[1]){
r1[i,] <- sort(r[i,])
r2[i,] <- rank(r[i,])
}
mik1=mak1=numeric(N)
for(k in 1:N){
tempr2 <- list()
for(i in 1: dim(C2)[1]){
tempr2[[k]] <- r2[i,k]
}
mik1[k] <- min(unlist(tempr2))
mak1[k] <- max(unlist(tempr2))
}
mik2<-sort(mik1);
mak2<-sort(mak1);
kl<-mik2[N*alpha/2]
ku<-mak2[N*(1-alpha/2)]
for( i in 1: dim(C2)[1]){
assign(paste0('the.',i,'th','lower.','limit'),round(get(paste0('r1'))[i,kl],6))
assign(paste0('the.',i,'th','upper.','limit'),round(get(paste0('r1'))[i,ku],6))
}
result$title1 <- "====================Method: GPQW===================="
result$title2 <- "The Simultaneous Confidence Intervals are: "
tempinterval <- list()
for(i in 1: dim(C2)[1]){
tempinterval[[i]] <- paste0('[',get(paste0('the.',i,'th','lower.','limit')),',',get(paste0('the.',i,'th','upper.','limit')),']')
}
interval0 <- do.call(rbind,tempinterval)
interval1 <- data.frame(interval0)
names(interval1) <- c('[LCL,UCL]')
result$interval <- interval1
t2 <- Sys.time()
result$star <- '**********************Time**************************'
result$t <- t2-t1;
result;
}
# result print func
GPQW<-function(n,p,mu,sigma,N,C2=rbind(c(-1,1,0),c(-1,0,1),c(0,-1,1)) ,alpha=0.05)
{
GPQW1<-GPQW0(n,p,mu,sigma,N,C2,alpha);
for(i in c('title1','title2','interval', 'star',"t"))
{
print(GPQW1[[i]])
}
}
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