R/DispNominal.R

In dco61/isteahMAT104: MAT104 Probabilité et Statistiques

#'
#'Dispersion measures for nominal data
#'@param x a numeric or character vector
#'@return vector containing VarRat,DMM,IVQ,IER,and ETM
#'@examples
#'m1 <- DispNominal(sample(1:7,200,replace=TRUE))
#'m2 <- DispNominal(sample(LETTERS[1:7],200, replace=TRUE))
#'@export
DispNominal <- function(x) {
    if (missing(x))
        stop("The x argument is required.")
    if (!is.vector(x))
        x <- as.vector(x)
    md <- Mode(x)
    nomd <- length(md)
    tbl <- table(x)
    N <- sum(tbl)
    k <- length(tbl)
    VarRat <- 1 - nomd * max(tbl)/N
    xs <- sort(tbl, descending = FALSE)
    DMM <- 1 - (sum(xs[k] - xs[1:k - 1]))/(N * (k - 1))
    IVQ <- (k/(k - 1)) * (1 - sum((tbl/N)^2))
    IER <- -sum((tbl/sum(tbl)) * log(tbl/sum(tbl)))/log(k)
    ETM <- 1 - sqrt(1/((k - 1) * N^2) * sum((xs[k] - xs)^2))
    out <- c(VarRat, DMM, IVQ, IER, ETM)
    return(out)
}