添加95％置信区间累积情节

Question

我想补充一个抛物线线，使用R表示95％置信区间，以这种抛硬币的情节：

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

这里是什么，我正在寻找一个例子：

更新： @ bill_080的回答非常好。不过我已经计算出100000次掷硬币：

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

，我真的想只是95％的限制添加到情节：

plot.ts(cumsum(100ktoss)) 

花了几个小时来计算我的100K掷硬币和当我尝试复制@ bill_080的代码时，内存不足（100,000）。

最后更新：好的。最后的问题。我在一张单曲线图上画出了几轮累计点击率，每一轮的开始时间都是零（实际上是1或-1，具体取决于输赢）。

>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。 现在解决了：

@ 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，因此您可以轻松地添加更多计算。

#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个==================================== ======================

如果你只是想绘制+/- 5％的线，它只是一个平方根函数。下面的代码：

#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，图必须存在。使用一些相同的变量作为编辑1中的代码：

#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