[R] Sampling from a population

[Mario Sendra Pina]

  Suppose you have a population of N <- 5 observations, x <- c(43, 28, 7, 61, 39). From that you can draw a maximum of 10 samples without replacement of size n <- 3. (Command choose(N,n) yields 10). For instance the samples I seek are

      43, 61, 7
      39, 7, 28  ...etc

  How can I get R to do that for me, to get an exhaustive list of samples of size n drawn without replacement from a population of size N?  The command, sample(x, 3, replace=FALSE), works well for one draw. Is there a package that will handle multiple draws?


  # First solution

  combix<-function(x,r) {
  n<-length(x)
  total<-choose(n,r)
  a<-matrix(0,total,r)
  ind<-c(1:r)
  for (i in 1:total){
     for (j in 1:r){a[i,j]<-x[ind[j]]}
     for (j in r:1){
          miro<-j
          ind[j]<-ind[j]+1
     if (ind[j]<n-r+j+1) break()
  }
     while(miro<r) {
     ind[miro+1]<-ind[miro]+1
      miro<-miro+1
        }
  }
  return(a)
  }

  print(combix(x=1:5,r=3))


  x<-c(8,3,1,11,4,7)
  print(mean(x))


  medias<- apply(combix(x,2),1,mean)
  print(mean(medias))



  #With-Replacement

  combixr<-function(x,r) {
  n<-length(x)
  total<-n**r
  a<-matrix(0,total,r)
  ind<-rep(1,r)
  for (i in 1:total){
     for (j in 1:r){a[i,j]<-x[ind[j]]}
     for (j in r:1){
          miro<-j
          ind[j]<-ind[j]+1
     if (ind[j]<n+1) break()
  }
     while(miro<r) {
     ind[miro+1]<-1
      miro<-miro+1
        }
  }
  return(a)
  }
  print(combixr(x=1:5,r=3))


  x<-c(8,3,1,11,4,7)
  print(mean(x))


  medias<- apply(combixr(x,2),1,mean)
  mean(medias)





  #Other form


  darcombi<- function(N,n,caso){
  vecpeq<-rep(0,n)
  ante<-0
  ante1<-0
  for(i in 1:n){
  N1<- N-(ante1+1)
  n1<- n-i
  v1<-cumsum(choose(N1:n1,n1))
  ante<-min(which(caso<=v1))
  vecpeq[i]<-ante+ante1
  resta<-0
  if (ante>1) resta<-v1[ante-1]
  caso<-caso-resta
  ante1<-vecpeq[i]
  }
  return(vecpeq)
  }

  N<-5
  n<-3

  for (i in 1:choose(N,n)){
  print(darcombi(N=N,n=n,i))
  }



  x <- c(43, 28, 7, 61, 39)
  N<-length(x)
  n<-3

  for (i in 1:choose(N,n)){
  print(x[darcombi(N=N,n=n,i)])
  }
      
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