R/CoefF.R

In biometryhub/RSS_package: Easing the Application of Ranked Set Sampling in Practice

#' This function computes the coefficient of variance estimator
#'
#' @param H Set size for each ranking group.
#' @param n Sample size.
#'
#' @return
#' @keywords internal

calculate_coefficients <- function(H, n) {
  kv <- 1:H
  ######################################################
  # Expected value of I_1^2/d_n^2    ###################
  E.I2.dn2 <- sum((kv / H)^(n - 1)) / H^2
  ######################################################

  ######################################################
  # Compute the expected value I_1^2/(n_1 d_n^2)      ##
  ######################################################
  indM <- rep(0, 3)
  for (k in (2:H)) {
    AA <- expand.grid((1:(k - 1)), 1:(n - k + 1))
    TEm <- cbind(rep(k, dim(AA)[1]), AA)
    indM <- rbind(indM, TEm)
  }
  indM <- indM[-1, ]
  indM <- as.matrix(indM)
  triplesum <- apply(indM, 1, TRIPLEF, n = n, H = H)
  E.I2.n1dn2 <- (1 / n + sum(triplesum)) / H^n

  # E.I2.n1dn2 <- (1/H^n)*(1/n+tot)
  ######################################################
  ######################################################
  VarI1.dn <- E.I2.dn2 - (1 / H^2)
  coef1D0 <- 1 / (H^2) - VarI1.dn / (H - 1)
  coef2D0 <- VarI1.dn
  coef3D0 <- E.I2.n1dn2 - VarI1.dn

  CoefD0 <- c(coef1D0, coef2D0, coef3D0)
  return(CoefD0)
}