# Gini Coefficient, Lorenz Curve, Lorenz Asymmetry Coefficient を計算する関数
lorenz <- function(x){	# http://www2.dmu.dk/1_om_dmu/2_afdelinger/3_teri/4_personlig/5_cfd/Download/ec00.pdf
	stopifnot(x >= 0)	# check sample
	n <- length(x <- sort(x))	# number of sample and sort
	x <- x / sum(x)	# convert to relative abundance
	l <- cumsum(x)	# cumulative abundance
	u <- mean(x)	# mean species size
	m <- sum(u>x)	# number of species with size less than u
	if (a <- sum(u==x)) {	# species with size equal to mean size exist?
		int.1 <- m/n + l[m]/l[n]
		int.2 <- (m+a)/n + l[m+a]/l[n]
		asym <- c(int.1, int.2)	# Lorenz asymmetry coefficient
		names(asym) <- c("min","max")
	} else {
		d <- (u-x[m]) / (x[m+1]-x[m])
		fu <- (m+d) / n
		lu <- (l[m]+d*x[m+1]) / l[n]
		asym <- sum(fu, lu)	# Lorenz asymmetry coefficient
	}
	axis.x <- seq(0, 1, length=n+1)
	axis.y <- c(0, l)
	gini <- (2*sum(axis.x-axis.y) / n)	# gini.coefficient
	u.gini <- gini * n / (n-1)	# unbiased estimator
	curve <- data.frame(axis.x, axis.y)	# lorenz curve
	list(gini.coefficient=gini, unbiased.gini=u.gini, asymmetry.coefficient=asym, lorenz.curve=curve)
}

# 使用方法
dat1 <- c(rep(5.55556, 9), 50)
dat2 <- c(rep(2,5), rep(18,5))
dat3 <- c(1,2,3,3,4,5)
lorenz(dat1)	# dat1とdat2で Gini Coefficient は同じであるものの
lorenz(dat2)	# Lorenz Asymmetry Coefficient は異なる
lorenz(dat3)	# 平均値と同じ値がある場合は、Lorenz Asymmetry Coefficient は点ではなく範囲で出力される