R/ineq.R

In ineq: Measuring Inequality, Concentration, and Poverty

ineq <- function(x, parameter = NULL, type=c("Gini", "RS", "Atkinson", "Theil",
    "Kolm", "var", "square.var", "entropy"), na.rm = TRUE)
{
  switch(match.arg(type),
  Gini = Gini(x, na.rm = na.rm),
  RS = RS(x, na.rm = na.rm),
  Atkinson = Atkinson(x, parameter = parameter, na.rm = na.rm),
  Theil = Theil(x, parameter = parameter, na.rm = na.rm),
  Kolm = Kolm(x, parameter = parameter, na.rm = na.rm),
  var = var.coeff(x, na.rm = na.rm),
  square.var = var.coeff(x, square=TRUE, na.rm = na.rm),
  entropy = entropy(x, parameter = parameter, na.rm = na.rm))
}

Gini <- function(x, corr = FALSE, na.rm = TRUE)
{
    if(!na.rm && any(is.na(x))) return(NA_real_)
    x <- as.numeric(na.omit(x))
    n <- length(x)
    x <- sort(x)
    G <- sum(x * 1L:n)
    G <- 2 * G/sum(x) - (n + 1L)
    if (corr) G/(n - 1L) else G/n
}

RS <- function(x, na.rm = TRUE)
{
    if(!na.rm && any(is.na(x))) return(NA_real_)
    x <- as.numeric(na.omit(x))
    d <- abs(x - mean(x))
    d <- mean(d)/(2*mean(x))
    d
}

Atkinson <- function(x, parameter = 0.5, na.rm = TRUE)
{
    if(!na.rm && any(is.na(x))) return(NA_real_)
    x <- as.numeric(na.omit(x))
    if(is.null(parameter)) parameter <- 0.5
    if(parameter==1)
        A <- 1 - (exp(mean(log(x)))/mean(x))
    else
        {
            x <- (x/mean(x))^(1-parameter)
            A <- 1 - mean(x)^(1/(1-parameter))
        }
    A
}

var.coeff <- function(x, square=FALSE, na.rm = TRUE)
{
    if(!na.rm && any(is.na(x))) return(NA_real_)
    x <- as.numeric(na.omit(x))
    n <- length(x)
    V <- sqrt((n-1)*var(x)/n)/mean(x)
    if(square) V <- V^2
    V
}

Theil <- function(x, parameter = 0, na.rm = TRUE)
{
  if(!na.rm && any(is.na(x))) return(NA_real_)
  x <- as.numeric(na.omit(x))
  if(is.null(parameter)) parameter <- 0
  if(parameter==0)
  {
    x <- x[!(x==0)]
    Th <- x/mean(x)
    Th <- sum(x*log(Th))
    Th <- Th/sum(x)
  }
  else
  {
    Th <- exp(mean(log(x)))/mean(x)
    Th <- -log(Th)
  }
  Th
}

Kolm <- function(x, parameter = 1, na.rm = TRUE)
{
  if(!na.rm && any(is.na(x))) return(NA_real_)
  x <- as.numeric(na.omit(x))
  x <- as.numeric(x)
  if(is.null(parameter)) parameter <- 1
  KM <- parameter * (mean(x)-x)
  KM <- mean(exp(KM))
  KM <- (1/parameter)*log(KM)
  KM
}

entropy <- function(x, parameter = 0.5, na.rm = TRUE)
{
  if(!na.rm && any(is.na(x))) return(NA_real_)
  x <- as.numeric(na.omit(x))
  x <- as.numeric(x)
  if(is.null(parameter)) parameter <- 0.5
  if(parameter==0)
    e <- Theil(x, parameter = 1)
  else
  if(parameter==1)
    e <- Theil(x, parameter = 0)
  else
  {
    k <- parameter
    e <- (x/mean(x))^k
    e <- mean(e-1)/(k*(k-1))
  }
  e
}