计算R中两条Lorenz曲线(可能相交)之间的面积

library(ggplot2)
library(dplyr)

# 创建数据
x <- seq(0, 1, length.out = 100) # x轴数据
y1 <- x^2 # 第一条Lorenz曲线
y2 <- 2*x^2 # 第二条Lorenz曲线
df <- data.frame(x, y1, y2) # 创建数据框

# 绘制Lorenz曲线图
ggplot(df, aes(x = x)) +
  geom_line(aes(y = y1, color = "Lorenz Curve 1")) +
  geom_line(aes(y = y2, color = "Lorenz Curve 2")) +
  labs(x = "Cumulative Percentile", y = "Cumulative Income Percentile") +
  scale_color_manual(values = c("Lorenz Curve 1" = "blue", "Lorenz Curve 2" = "red")) +
  theme_minimal()

# 计算两条曲线之间的面积
area <- sum(abs(df$y1 - df$y2)) / 2