R/cRangeNor.R

In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

cRangeNor<-function(alpha,k){

  r<-function(x,n){
  	inner.int<-function(s){
  		exp(-s^2)*(pnorm(s+x/2)-pnorm(s-x/2))^(n-2)
  	}
  	return(n*(n-1)*exp(-x^2/4)/(2*pi)*integrate(inner.int,-Inf,Inf)$value)
  }

  approx.dens<-test.grid<-seq(0,10,.001)
  for(i in 1:length(test.grid)){
  	approx.dens[i]<-r(test.grid[i],k)*.001
  }
  approx.dens=approx.dens/sum(approx.dens)
  upper.tails<-rev(cumsum(rev(approx.dens)))
  test.grid[min(which(upper.tails<=alpha))]
}