向累积图添加 95% 置信限

Question

我想使用 R 在这个抛硬币图上添加一条表示 95% 置信限的抛物线：

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：

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

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

我真的很想在该图中添加 95% 的限制：

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）。

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）。

>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：

@bill_080 非常感谢。这是最终产品：

Answer 1

试试这个。所有循环都是for循环，所以你可以轻松添加更多计算。

#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 ============================================== ==============

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：

#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 ============================================= =====

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：

#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