R/cucconi.teststat.R

In tpepler/nonpar: Collection of methods for non-parametric analysis

cucconi.teststat <- function(x, y, m = length(x), n = length(y)){
  
  # Calculates the test statistic for the Cucconi two-sample location-scale test
  
  N <- m + n
  S <- rank(c(x, y))[(m + 1):N]
  denom <- sqrt(m * n * (N + 1) * (2 * N + 1) * (8 * N + 11) / 5)
  U <- (6 * sum(S^2) - n * (N + 1) * (2 * N + 1)) / denom
  V <- (6 * sum((N + 1 - S)^2) - n * (N + 1) * (2 * N + 1)) / denom
  rho <- (2 * (N^2 - 4)) / ((2 * N + 1) * (8 * N + 11)) - 1
  C <- (U^2 + V^2 - 2 * rho * U * V) / (2 * (1 - rho^2))
  return(C)
}