在直方图中说明标准偏差

Question

考虑以下简单示例：

# E. Musk in Grunheide 
set.seed(22032022) 

# generate random numbers 
randomNumbers <- rnorm(n = 1000, mean = 10, sd = 10)

# empirical sd 
sd(randomNumbers)
#> [1] 10.34369

# histogram 
hist(randomNumbers, probability = TRUE, main = "", breaks = 50)

# just for illusatration purpose 
###
# empirical density 
lines(density(randomNumbers), col = 'black', lwd = 2)
# theortical density 
curve(dnorm(x, mean = 10, sd = 10), col = "blue", lwd = 2, add = TRUE)
###

^{由 reprex package (v2.0.1)}

创建于 2022-03-22

问题： 有没有一种很好的方法可以通过颜色说明直方图中的经验标准偏差（sd）？例如。用不同的颜色表示内部条形，或在 x 轴上用区间表示 sd 的范围，即 [mean +/- sd]？

请注意，如果 ggplot2 提供了一个简单的解决方案，也将不胜感激。

Answer 1

这是一个ggplot解决方案。先计算mean和sd，将值保存在不同的vector中。然后使用 ifelse 语句将值分类为“范围内”和“范围外”，fill 它们具有不同的颜色。

蓝线代表您问题中所述的正态分布，黑线代表我们绘制的直方图的密度图。

library(ggplot2)

set.seed(22032022) 

# generate random numbers 
randomNumbers <- rnorm(n=1000, mean=10, sd=10)

randomNumbers_mean <- mean(randomNumbers)
randomNumbers_sd <- sd(randomNumbers)

ggplot(data.frame(randomNumbers = randomNumbers), aes(randomNumbers)) +
  geom_histogram(aes(
    fill = ifelse(
      randomNumbers > randomNumbers_mean + randomNumbers_sd |
        randomNumbers < randomNumbers_mean - randomNumbers_sd,
      "Outside range",
      "Within range"
    )
  ), 
  binwidth = 1, col = "gray") +
  geom_density(aes(y = ..count..)) + 
  stat_function(fun = function(x) dnorm(x, mean = 10, sd = 10) * 1000,
                color = "blue") +
  labs(fill = "Data")

^{由 reprex package (v2.0.1)}

创建于 2022-03-22

Answer 2

这与 Benson 的回答类似 ggplot 解决方案，除了我们预先计算直方图并使用 geom_col，这样我们就不会在 sd 边界处得到任何不受欢迎的堆叠：

# E. Musk in Grunheide 
set.seed(22032022) 

# generate random numbers 
randomNumbers <- rnorm(n=1000, mean=10, sd=10)

h <- hist(randomNumbers, breaks = 50, plot = FALSE)

lower <- mean(randomNumbers) - sd(randomNumbers)
upper <- mean(randomNumbers) + sd(randomNumbers)

df <- data.frame(x = h$mids, y = h$density, 
                 fill = h$mids > lower & h$mids < upper)

library(ggplot2)

ggplot(df) +
  geom_col(aes(x, y, fill = fill), width = 1, color = 'black') +
  geom_density(data = data.frame(x = randomNumbers), 
               aes(x = x, color = 'Actual density'),
               key_glyph = 'path') +
  geom_function(fun = function(x) {
    dnorm(x, mean = mean(randomNumbers), sd = sd(randomNumbers)) },
    aes(color = 'theoretical density')) +
  scale_fill_manual(values = c(`TRUE` = '#FF374A', 'FALSE' = 'gray'), 
                    name = 'within 1 SD') +
  scale_color_manual(values = c('black', 'blue'), name = 'Density lines') +
  labs(x = 'Value of random number', y = 'Density') +
  theme_minimal()

Answer 3

data.frame(rand = randomNumbers,
           cut = {
             sd <- sd(randomNumbers)
             mn <- mean(randomNumbers)
             cut(randomNumbers, c(-Inf, mn -sd, mn +sd, Inf))
           }) |>
  ggplot(aes(x = rand, fill = cut ) ) +
  geom_histogram()

在直方图中说明标准偏差

Illustrate standard deviation in histogram

r

ggplot2

histogram