Reconstruction of the distinctiveness measure from Murdock 1960 paper

murdock.R

murdock_D <- function(x, pc = T) {
  n <- length(x)
  mr <- matrix(x, nrow = n, ncol = n)
  mc <- matrix(x, nrow = n, ncol = n, byrow = T)
  md <- abs(mr - mc)
  td <- rowSums(md)
  dpc <- td / sum(td)
  if (pc) {
    # percentages or D%
    return(dpc)
  } else {
    # total distinctiveness or TD
    return(td)
  }
}
# simple test case
murdock_D(1:3)
# isolated values get to 50%
murdock_D(c(0,0.1, 10))
# should be 30:20:20:30
murdock_D(c(2,4,6,8))
# should be wrong
murdock_D(1:8)
# almost correct
murdock_D(log(1:8))
# same
murdock_D(log10(1:8)) 
# wrong
murdock_D(log(1:9))
# random set of five
murdock_D(c(121, 202, 205, 37, 207))

# Murdock, B. B. (1960). The distinctiveness of stimuli. Psychological Review, 67(1), 16–31. https://doi.org/10.1037/h0042382