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#' Brewer sampling procedure --------------------------------------------------
#'
#' @param pik vector of first-order inclusion probabilities
#' @param n sample size
#' @param N population size
#' @param s vector of length N, with 1s at the positions of self-selecting units
#' @param list vector with positions of self selcting units
#'
#'
#' @note this function is a modified version of function \code{\link[sampling]{UPbrewer}},
#' from the \pkg{sampling} package.
#'
#' @keywords internal
brewer <- function(pik, n, N, s, list){
sb <- rep(0, N)
for (j in 1:n) {
a <- sum(pik * sb)
p <- (1 - sb) * pik * ((n - a) - pik)/((n - a) - pik * (n - j + 1))
p <- p/sum(p)
p <- cumsum(p)
u <- runif(1)
# for (h in seq_along(p)){
# if (u < p[h]) break
# }
h <- which(u<p)[1]
sb[h] <- 1
}
s[list] <- sb
return(s)
}
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