Question

我有两个相关变量x和y，我想知道如何在R中找到它们的经验联合CDF？

此外，我们如何找到概率：P（X <= 2和Y <= 3），P（X> = 2和Y> = 3），P（X> = 3和Y <= 2），P（X <= 3并且Y> = 2）; P（X <= 2或Y <= 3），P（X> = 3或Y> = 2），P（X> = 3或Y <= 2），P（X <= 2或Y> = 3 ）？感谢您的帮助。

x= c(1,3,2,2,8,2,1,3,1,1,3,3,1,1,2,1,2,1,1,3,4,1,1,3,1,1,2,1,3,7,1,4,6,1,2,1,1,3,1,2,2,3,4,1,1,1,1,2,2,12,1,1,2,1,1,1,3,4)
y = c(1.42,5.15,2.52,2.29,12.36,2.82,1.49,3.53,1.17,1.03,4.03,5.26,1.65,1.41,3.75,1.09,3.44,1.36,1.19,4.76,5.58,1.23,2.29,7.71,1.12,1.26,2.78,1.13,3.87,15.43,1.19,4.95,7.69,1.17,3.27,1.44,1.05,3.94,1.58,2.29,2.73,3.75,6.80,1.16,1.01,1.00,1.02,2.32,2.86,22.90,1.42,1.10,2.78,1.23,1.61,1.33,3.53,10.44)

cor(x,y)
x_cdf = ecdf(x)
y_cdf = ecdf(y)

Answer 1

您可以使用mltools软件包。

x <- c(1,3,2,2,8,2,1,3,1,1,3,3,1,1,2,1,2,1,1,3,4,1,1,3,1,1,2,1,3,7,1,4,6,1,2,1,1,3,1,2,2,3,4,1,1,1,1,2,2,12,1,1,2,1,1,1,3,4)
y <- c(1.42,5.15,2.52,2.29,12.36,2.82,1.49,3.53,1.17,1.03,4.03,5.26,1.65,1.41,3.75,1.09,3.44,1.36,1.19,4.76,5.58,1.23,2.29,7.71,1.12,1.26,2.78,1.13,3.87,15.43,1.19,4.95,7.69,1.17,3.27,1.44,1.05,3.94,1.58,2.29,2.73,3.75,6.80,1.16,1.01,1.00,1.02,2.32,2.86,22.90,1.42,1.10,2.78,1.23,1.61,1.33,3.53,10.44)

library(mltools)
library(data.table)

# set data in a data.table
dt <- data.table(x = x, y = y)

示例：P(X <= 3, Y <= 5) = ?

> empirical_cdf(dt, ubounds = data.table(x = 3, y = 5))
   x y N.cum       CDF
1: 3 5    47 0.8103448
> mean(x <= 3 & y <= 5) # same result
[1] 0.8103448

现在，假设您要计算P(X > 3, Y <= 5)。从平等开始

P(X <= 3, Y <= 5) + P(X > 3, Y <= 5) = P(Y <= 5)

你得到

P(X > 3, Y <= 5) = P(Y <= 5) - P(X <= 3, Y <= 5)

然后您按以下方式计算此概率：

> empirical_cdf(dt$y, 5)$CDF - empirical_cdf(dt, data.table(x = 3, y = 5))$CDF
[1] 0.01724138
> mean(x > 3 & y <= 5) # same result
[1] 0.01724138

如何在R中找到多元经验累积分布函数（CDF）？

1 个答案: