搜索以查找覆盖曲线下95％面积的两个数字 [英] Search to find two numbers that cover 95% of the area under a curve

问题描述

我有两列数字（列 dd ）和列 strong> yy ，请参阅下面的链接以访问此数据）。当我针对 yy （ Y轴）绘制dd（ X轴）时， ：

plot（dd，yy，ty =l，xlab =dd，ylab =yy，lwd = 2， xaxs =i）

我得到这个：

编码问题：

移动从 - Inf改为0 u ，直到其他点覆盖此曲线下面积的95％？ 换句话说，如果箭头覆盖此曲线下方95％的面积，我们希望看到与两个箭头指示符对应的两个数字？

以下是 R代码，可轻松将这些小数据导入您的Rstudio：

  id<  - 0B5V8AyEFBTmXM1VIYUYxSG5tSjQ
 
 Data<  -  read.csv（paste0（https://docs.google.com/uc?id =，id，& export = download））
  

解决方案

编辑：我以前的近似值不是很准确。事实证明， pracma 包有一个函数， cumtrapz ，它接近梯形积分并输出每个点的和从左边开始。使用该函数可以给出更准确的答案。

  library（pracma）
 points<  -  read.csv（paste0 （https://docs.google.com/uc?id=\",id,\"&export=download））
区域<  -  cumtrapz（积分$ dd，积分$ yy）
 ind < -  rev（其中（面积[面积（面积）]  - 面积> 0.95））[1] 
 
点< - 点数$ dd [ind] 
 point 
 
＃[1] -0.06406406 
  

Background:

I have two columns of numbers (column "dd", and column "yy", see below to access this data). When I plot "dd" (X-axis) against "yy" (Y-axis), using:

plot(dd, yy, ty="l", xlab = "dd", ylab ="yy", lwd=2, xaxs="i")

I get this:

Coding question:

Moving from "-Inf" to "0" up until what other point covers 95% of the area under this curve? In other words, we want to see the two numbers that correspond to the two ARROW HEADS TIPS if the arrow is to cover 95% of the area under this curve?

Here is the R code to easily import this small data into your Rstudio:

id <- "0B5V8AyEFBTmXM1VIYUYxSG5tSjQ"

Data <- read.csv(paste0("https://docs.google.com/uc?id=",id,"&export=download")) 

解决方案

Edit: My previous approximation was not very accurate. It turns out the pracma package has a function, cumtrapz, which approximates integrals with trapezoids and outputs the sum at each point starting from the left. Using that function gives a more accurate answer.

library(pracma)
points <- read.csv(paste0("https://docs.google.com/uc?id=",id,"&export=download")) 
area   <- cumtrapz(points$dd, points$yy)
ind    <- rev(which(area[length(area)] - area > .95))[1]

point  <- points$dd[ind]
point

# [1] -0.06406406

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