rm(list=ls(all=T))

# Daten einlesen
data_w <- scan("D://Uebungen//2010_Sommersemester//Wirtschaftsstatistik_SS_10//Blatt 4//einkommen_w.txt")
data_m <- scan("D://Uebungen//2010_Sommersemester//Wirtschaftsstatistik_SS_10//Blatt 4//einkommen_m.txt")

# Lage- und Streuungsmasszahlen
summary(data_w)
summary(data_m)
sd(data_w)
sd(data_m)
length(data_w[data_w<2.657]) / length(data_w)
length(data_m[data_m<2.657]) / length(data_m)

# Lorenzkurven
# Frauen
# x-Koordinaten der Lorenzkurve
u_w <- seq(1/length(data_w), 1, 1/length(data_w))
# y-Koordinaten der Lorenzkurve
v_w <- rep(0, length(data_w))
for (j in 1:length(data_w)) {
	v_w[j] = sum(data_w[1:j]) / sum(data_w)
}
# Männer
# x-Koordinaten der Lorenzkurve
u_m <- seq(1/length(data_m), 1, 1/length(data_m))
# y-Koordinaten der Lorenzkurve
v_m <- rep(0, length(data_m))
for (j in 1:length(data_m)) {
	v_m[j] = sum(data_m[1:j]) / sum(data_m)
}
# plotten
plot(u_w, v_w, type = "l", xlab = "u", ylab = "v")
lines(u_m, v_m, type = "l", lty = 2)
legend(x = 0.1, y = 0.9, legend = c("Männer", "Frauen"), lty = c(2, 1))

# Gini-Koeffizienten
# Frauen
p_w <- data_w / sum(data_w)
gamma_w <- (2*sum(seq(1:length(data_w))*p_w) - (length(data_w)+1)) / length(data_w)
gamma_w
# Männer
p_m <- data_m / sum(data_m)
gamma_m <- (2*sum(seq(1:length(data_m))*p_m) - (length(data_m)+1)) / length(data_m)
gamma_m

# Histogramme
par(mfrow = c(2, 2))
hist(data_w, freq = FALSE)
hist(data_m, freq = FALSE)
hist(data_w[data_w<10], freq = FALSE)
hist(data_m[data_m<10], freq = FALSE)

# Kontingenztafel relative Häufigkeit Einkommen < 2000 vs. Einkommen >= 2000
length(data_w[data_w<2]) / (length(data_w) + length(data_m))
length(data_w[data_w>=2]) / (length(data_w) + length(data_m))
length(data_m[data_m<2]) / (length(data_w) + length(data_m))
length(data_m[data_m>=2]) / (length(data_w) + length(data_m))