以均匀分布为例

set.seed(42) m <- 10000 # 随机数个数 n <- 1000 # 重复次数 x <- replicate(n, sum(runif(m))) # 重复n次并求和 y <- (x - mean(x)) / sd(x) # 标准化 hist(y, freq = FALSE, ylim = c(0, 0.4), main = "Uniform Distribution") # 绘制频率分布直方图 curve(dnorm(x), add = TRUE, col = "blue", lwd = 2) # 叠加标准正态分布密度曲线 lines(density(y), col = "red", lwd = 2) # 叠加核密度估计曲线

使用Q-Q图

qqnorm(y) qqline(y, col = "red")

以指数分布为例

set.seed(42) m <- 10000 # 随机数个数 n <- 1000 # 重复次数 x <- replicate(n, sum(rexp(m))) # 重复n次并求和 y <- (x - mean(x)) / sd(x) # 标准化 hist(y, freq = FALSE, ylim = c(0, 0.4), main = "Exponential Distribution") # 绘制频率分布直方图 curve(dnorm(x), add = TRUE, col = "blue", lwd = 2) # 叠加标准正态分布密度曲线 lines(density(y), col = "red", lwd = 2) # 叠加核密度估计曲线

使用Q-Q图

qqnorm(y) qqline(y, col = "red")

以二项分布为例

set.seed(42) m <- 100 # 随机数个数 n <- 1000 # 重复次数 x <- replicate(n, sum(rbinom(m, size = 10, prob = 0.5))) # 重复n次并求和 y <- (x - mean(x)) / sd(x) # 标准化 hist(y, freq = FALSE, ylim = c(0, 0.4), main = "Binomial Distribution") # 绘制频率分布直方图 curve(dnorm(x), add = TRUE, col = "blue", lwd = 2) # 叠加标准正态分布密度曲线 lines(density(y), col = "red", lwd = 2) # 叠加核密度估计曲线

使用Q-Q图

qqnorm(y) qqline(y, col = "red")

以泊松分布为例

set.seed(42) m <- 100 # 随机数个数 n <- 1000 # 重复次数 x <- replicate(n, sum(rpois(m, lambda = 2))) # 重复n次并求和 y <- (x - mean(x)) / sd(x) # 标准化 hist(y, freq = FALSE, ylim = c(0, 0.4), main = "Poisson Distribution") # 绘制频率分布直方图 curve(dnorm(x), add = TRUE, col = "blue", lwd = 2) # 叠加标准正态分布密度曲线 lines(density(y), col = "red", lwd = 2) # 叠加核密度估计曲线

使用Q-Q图

qqnorm(y) qqline(y, col = "red")

以柯西分布为例

set.seed(42) m <- 10000 # 随机数个数 n <- 1000 # 重复次数 x <- replicate(n, sum(rcauchy(m))) # 重复n次并求和 y <- (x - mean(x)) / sd(x) # 标准化 hist(y, freq = FALSE, ylim = c(0, 0.2), main = "Cauchy Distribution") # 绘制频率分布直方图 curve(dnorm(x), add = TRUE, col = "blue", lwd = 2) # 叠加标准正态分布密度曲线 lines(density(y), col = "red", lwd = 2) # 叠加核密度估计曲线

使用Q-Q图

qqnorm(y) qqline(y, col = "red"