如何获取R中两个交叉ECDF的交点?

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英文:

How can I get the intersection point of two crossing ecdfs in R?

问题

我使用以下代码制作了两个ECDF图:

ecdf1 <- ecdf(data1)
ecdf2 <- ecdf(data2)

这些图相互交叉。我需要获取它们的交点坐标。我应该如何在R中实现这一点?

英文:

I have two ecdf plots using below code:

ecdf1 &lt;- ecdf(data1)
ecdf2 &lt;- ecdf(data2)

These plots are crossing each other. I need to take the crossing point (intersection point) coordinates. How should I do this in R?

答案1

得分: 8

以下是代码的翻译部分:

set.seed(1)

data1 <- rnorm(50) + 1.2
data2 <- rexp(50)

现在我们使用您的代码创建两个ecdf函数:

ecdf1 <- ecdf(data1)
ecdf2 <- ecdf(data2)

如果我们绘制它们,我们会看到这些曲线在两个点处相交:一次在0和1之间,再次在略高于2处。

plot(ecdf1, col = "red")
plot(ecdf2, col = "blue", add = TRUE)

要找到这些确切的点,我们创建一个关于x的函数,该函数是两个ecdf函数在x处的差异。然后,我们使用uniroot函数确定此差异函数等于0的位置:

diff_func <- function(x) ecdf1(x) - ecdf2(x)

root1 <- uniroot(diff_func, c(0, 1))$root # 找到较低的交点
root2 <- uniroot(diff_func, c(2, 3))$root # 找到较高的交点

我们可以检查我们的结果是否合理:

root1
#> [1] 0.1568627
root2
#> [1] 2.055556

甚至可以绘制线段以演示这些交点是正确的:

segments(root1, y0 = 0, y1 = ecdf1(root1), lty = 2)
segments(root2, y0 = 0, y1 = ecdf1(root2), lty = 2)

创建于2023-02-26,使用 reprex v2.0.2

英文:

Lets' create a reproducible example to demonstrate:

set.seed(1)

data1 &lt;- rnorm(50) + 1.2
data2 &lt;- rexp(50)

Now we use your code to create the two ecdf functions:

ecdf1 &lt;- ecdf(data1)
ecdf2 &lt;- ecdf(data2)

If we plot them, we will see these curves intersect at two points: once between 0 and 1, and again just above 2.

plot(ecdf1, col = &quot;red&quot;)
plot(ecdf2, col = &quot;blue&quot;, add = TRUE)

如何获取R中两个交叉ECDF的交点?

To find these exact points, we create a function of x that is the difference between the two ecdf functions at x. We then use the function uniroot to determine where this difference function is equal to 0:

diff_func &lt;- function(x) ecdf1(x) - ecdf2(x)

root1 &lt;- uniroot(diff_func, c(0, 1))$root # Finds the lower intersection
root2 &lt;- uniroot(diff_func, c(2, 3))$root # Finds the upper intersection

We can check our results make sense:

root1
#&gt; [1] 0.1568627
root2
#&gt; [1] 2.055556

And even plot segments to demonstrate the intersections are correct:

segments(root1, y0 = 0, y1 = ecdf1(root1), lty = 2)
segments(root2, y0 = 0, y1 = ecdf1(root2), lty = 2)

如何获取R中两个交叉ECDF的交点?

<sup>Created on 2023-02-26 with reprex v2.0.2</sup>

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  • 本文由 发表于 2023年2月27日 05:34:45
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