在同一图中绘制正态分布和二项式分布

Question

正如标题所示，我正在尝试使用 R 在同一个图中绘制正态分布和二项式分布。我的尝试如下所示，我的正态分布看起来如此不正确有什么原因吗？我已经仔细检查了平均值和标准差，一切看起来都很好。

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

barplot(y, 
     col = 'lightblue',
     names.arg = x,
     main = 'Binomial distribution, n=151, p=.803')

range <- seq(mu - dev*sigma, mu + dev*sigma, 0.01)
height <- dnorm(range, mean = mu, sd = sigma) 
lines(range, height, col = 'red', lwd = 3)

Answer 1

barplot 对您的情况来说是错误的功能。或者，如果您真的想使用它，则必须在 barplot 和 lines 之间重新调整 x 轴

barplot 的默认值是将每个 height 值放在

head(c(barplot(y, plot = FALSE)))
# [1] 0.7 1.9 3.1 4.3 5.5 6.7

这可以通过您选择 space 和 width 或两者的组合来更改

head(c(barplot(y, plot = FALSE, space = 0)))
# [1] 0.5 1.5 2.5 3.5 4.5 5.5

head(c(barplot(y, plot = FALSE, space = 0, width = 3)))
# [1]  1.5  4.5  7.5 10.5 13.5 16.5

您可以使用plot 来避免处理这些事情

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

plot(x, y, type = 'h', lwd = 10, lend = 3, col = 'lightblue',
     ann = FALSE, las = 1, bty = 'l', yaxs = 'i', ylim = c(0, 0.08))
title(main = sprintf('Binomial distribution, n=%s, p=%.3f', n, p))
lines(x, dnorm(x, mean = mu, sd = sigma), col = 'red', lwd = 7)

xx <- seq(min(x), max(x), length.out = 1000)
lines(xx, dnorm(xx, mean = mu, sd = sigma), col = 'white')

此图中的“条”取决于您选择的lwd 和您的设备尺寸，但如果您需要更好地控制它，您可以使用rect，这需要更多的工作。

w <- 0.75
plot(x, y, type = 'n', ann = FALSE, las = 1, bty = 'l', yaxs = 'i', ylim = c(0, 0.08))
rect(x - w / 2, 0, x + w / 2, y, col = 'lightblue')
lines(xx, dnorm(xx, mean = mu, sd = sigma), col = 'red', lwd = 3)
title(main = sprintf('Binomial distribution, n=%s, p=%.3f', n, p))

Answer 2

您可以使用ggplot2 包

library(ggplot2)

n <- 151
p <- 0.2409
mean <- n*p
sd <-   sqrt(n*p*(1-p))
binwidth <-   0.005


xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

df <- cbind.data.frame(x, y)

ggplot(df, aes(x = x, y = y)) +
  geom_bar(stat="identity", fill = 'dodgerblue3')+
  labs(title = "Binomial distribution, n=151, p=.803",
       x = "",
       y = "") +
  theme_minimal()+
  # Create normal curve, akousting for number of observations and binwidth
  stat_function( 
    fun = function(x, mean, sd, n, bw){ 
      dnorm(x = x, mean = mean, sd = sd)
    }, col = "red", size=I(1.4),  
    args = c(mean = mean, sd = sd, n = n, bw = binwidth))

Answer 3

您可以使用ggplot2 包来做到这一点（我对正态分布感到惊讶，但用 geom_point 替换 geom_line 让我确信它具有这种形式（方差是否太高？））：

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))

x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

z <- dnorm(x = qnorm(p = seq(0,1, length.out = length(x)), mean = mu, sd = sigma), mean = mu, sd = sigma)

library(magrittr)
library(ggplot2)
data.frame(x, y, z) %>% 
    ggplot(aes(x = x)) +
    geom_col(aes(y = y)) +
    geom_line(aes(x = x, y = z, colour = "red"),
          show.legend = FALSE)