将 95% 置信限添加到累积图 [英] Add 95% confidence limits to cumulative plot

问题描述

我想使用 R 向这个抛硬币图添加一条表示 95% 置信限的抛物线:

I would like to add a parabola line denoting 95% confidence limits to this coin toss plot using R:

x  <- sample(c(-1,1), 60000, replace = TRUE)
plot.ts(cumsum(x), ylim=c(-250,250))

这是我正在寻找的示例:

Here is an example of what I'm looking for:

更新:@bill_080 的回答非常好.但是我已经计算了 100,000 次抛硬币:

UPDATE: @bill_080's answer is excellent. However I have already calculated 100,000 coin tosses:

str(100ktoss)
num [1:100000] -1 1 1 1 -1 -1 1 -1 -1 -1 ...

我真的想在该图中添加 95% 的限制:

and I really want to just add the 95% limit to that plot:

plot.ts(cumsum(100ktoss))

计算我的 100,000 次抛硬币需要几个小时，当我尝试使用 @bill_080 的代码进行复制时，我的内存不足(对于 100,000 次).

It took several hours to calculate my 100K coin tosses and when I try and replicate with @bill_080's code I run out of memory (for 100,000).

最终更新:好的.最后一个问题.我在一个图表上绘制了几轮累积命中的图，每轮的开始都固定为零(实际上是 1 或 -1，取决于它是赢还是输).

FINAL UPDATE: Okay. Last problem. I have a plot of several rounds of cummulative hits, on a single graph with the start of each round clamped at zero (actually 1 or -1 depending on if it was a win or lose).

>str(1.ts)  
Time-Series [1:35] from 1 to 35: 1 2 1 2 3 4 5 4 5 6 ...  
>str(2.ts)  
Time-Series [1:150] from 36 to 185: -1 0 1 0 -1 -2 -1 0 1 2 ...  

我想为每个段添加相同的 95% 限制，就像这样.现已解决:

I would like to add the same 95% limit to each segment, like thus. Now solved:

@bill_080 非常感谢.这是最终产品:

@bill_080 Many thanks. This is the the end product:

推荐答案

试试这个.所有循环都是 for 循环，因此您可以轻松添加更多计算.

Try this. All loops are for loops, so you can easily add more calculations.

#Set the number of bets and number of trials and % lines
numbet <- 6000 #6000 bets
numtri <- 1000 #Run 1000 trials of the 6000 bets
perlin <- 0.05 #Show the +/- 5% lines on the graph
rantri <- 60 #The 60th trial (just a random trial to be drawn)

#Fill a matrix where the rows are the cumulative bets and the columns are the trials
xcum <- matrix(NA, nrow=numbet, ncol=numtri)
for (i in 1:numtri) {
  x <- sample(c(-1,1), numbet, replace = TRUE)
  xcum[,i] <- cumsum(x)
}

#Plot the trials as transparent lines so you can see the build up
matplot(xcum, type="l", xlab="Number of Bets", ylab="Cumulative Sum", main="Cumulative Results", col=rgb(0.01, 0.01, 0.01, 0.02))
grid()

#Sort the trials of each bet so you can pick out the desired %
xcumsor <- xcum
for (i in 1:numbet) {
  xcumsor[i,] <- xcum[i,order(xcum[i,])]
}

#Draw the upper/lower limit lines and the 50% probability line     
lines(xcumsor[, perlin*numtri], type="l", lwd=2, col=rgb(1, 0.0, 0.0)) #Lower limit
lines(xcumsor[, 0.5*numtri], type="l", lwd=3, col=rgb(0, 1, 0.0)) #50% Line
lines(xcumsor[, (1-perlin)*numtri], type="l", lwd=2, col=rgb(1, 0.0, 0.0)) #Upper limit

#Show one of the trials
lines(xcum[, rantri], type="l", lwd=1, col=rgb(1, 0.8, 0)) #Random trial

#Draw the legend
legend("bottomleft", legend=c("Various Trials", "Single Trial", "50% Probability", "Upper/Lower % Limts"), bg="white", lwd=c(1, 1, 3, 2), col=c("darkgray", "orange", "green", "red"))

编辑1 ============================================================

Edit 1 ==========================================================

如果您只是想绘制 +/- 5% 的线，它只是一个平方根函数.代码如下:

If you're just trying to draw the +/- 5% lines, it's just a square root function. Here's the code:

#Set the bet sequence and the % lines
betseq <- 1:100000 #1 to 100,000 bets
perlin <- 0.05 #Show the +/- 5% lines on the graph

#Calculate the Upper and Lower limits using perlin
#qnorm() gives the multiplier for the square root
upplim <- qnorm(1-perlin)*sqrt(betseq)
lowlim <- qnorm(perlin)*sqrt(betseq)

#Get the range for y
yran <- range(upplim, lowlim)

#Plot the upper and lower limit lines
plot(betseq, upplim, ylim=yran, type="l", xlab="", ylab="")
lines(betseq, lowlim)

编辑2 ==================================================

Edit 2 ==================================================

要在正确的位置添加抛物线，如果定义一个函数可能会更容易.请记住，因为新函数 (dralim) 使用 lines，所以在调用 dralim 之前绘图必须存在.使用一些与编辑 1 中的代码相同的变量:

To add the parabolas at the right locations, it is probably easier if you define a function. Keep in mind that because the new function (dralim) uses lines, the plot has to exist before you call dralim. Using some of the same variables as the code in Edit 1:

#Set the bet sequence and the % lines
betseq <- 0:700 #0 to 700 bets
perlin <- 0.05 #Show the +/- 5% lines on the graph

#Define a function that plots the upper and lower % limit lines
dralim <- function(stax, endx, perlin) {
  lines(stax:endx, qnorm(1-perlin)*sqrt((stax:endx)-stax))
  lines(stax:endx, qnorm(perlin)*sqrt((stax:endx)-stax))
}

#Build the plot area and draw the vertical dashed lines
plot(betseq, rep(0, length(betseq)), type="l", ylim=c(-50, 50), main="", xlab="Trial Number", ylab="Cumulative Hits")
abline(h=0)
abline(v=35, lty="dashed") #Seg 1
abline(v=185, lty="dashed") #Seg 2
abline(v=385, lty="dashed") #Seg 3
abline(v=485, lty="dashed") #Seg 4
abline(v=585, lty="dashed") #Seg 5

#Draw the % limit lines that correspond to the vertical dashed lines by calling the
#new function dralim.
dralim(0, 35, perlin) #Seg 1
dralim(36, 185, perlin) #Seg 2
dralim(186, 385, perlin) #Seg 3
dralim(386, 485, perlin) #Seg 4
dralim(486, 585, perlin) #Seg 5
dralim(586, 701, perlin) #Seg 6

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