R 为什么我对圆周率图的蒙特卡罗估计是空的

发布于02月19日

我正在做一个关于圆周率的蒙特卡罗近似的练习.

由于某种原因，当所有的变量都被定义时，曲线图是空的，你能帮我吗？

以下是代码:

set.seed(1) 

M = 10^4  

U = matrix(runif(2*M), ncol = 2) 

sum_squares = U[,1]^2 + U[,2]^2  
under_curve = sum_squares < 1 


points_under_curve = U[under_curve,] 
points_over_curve = U[!under_curve,] 

pi_4_estimate = sum(under_curve)/M
cat("Estimation of π/4 = ", pi_4_estimate)

pi_estimate = pi_4_estimate * 4
cat("Estimation of π = ", pi_estimate)


plot(pi_estimate, type = "l", xlab = "Number of Simulations", ylab = "Estimation of Pi", main = "Convergence of Monte Carlo Estimator of Pi", xlim = c(0,M))

Empty plot

I tried : check if the variables pi_4_estimate and pi_estimate are correctly calculated. Modifying the plot parameters
restarting RStudio and running the code again.

推荐答案

pi_estimate是接近圆周率的长度为-1的数值向量.当您try 将其绘制为一条线时，不会显示任何内容，因为一条线需要至少有两个点才能连接.

大概您想要展示的是，随着点数的增加，曲线下的点的比例如何逐渐接近pi/4.为此，您可以绘制under_curve的累积和除以沿under_curve的序列

set.seed(1) 

M <- 1e4 

sum_squares <- runif(M)^2 + runif(M)^2
under_curve <- sum_squares < 1 

estimator <- 4 * cumsum(under_curve) / seq_along(under_curve)

plot(estimator,
     type = "l", 
     xlab = "Number of Simulations", 
     ylab = "Estimation of Pi", 
     main = "Convergence of Monte Carlo Estimator of Pi", 
     xlim = c(0, M))

abline(h = pi, lty = 2)