如何可視化概率分佈函數之間的差異？

Question

我試着想象的分佈函數兩個柱狀圖之間的差異等方面的差異在以下兩條曲線：在彼此的頂部

當差異大，你可以只繪製兩條曲線和如上所述填補差異，但是當差異變得非常小時，這是麻煩的。繪製此的另一種方式，正在密謀的差異本身如下：

不過，這似乎很難讀給大家看這樣的圖是第一次，所以我想知道：有沒有用其他方式可以看到兩個分佈函數之間的區別？

Answer 1

我想也許這可能是一個選擇，只是簡單地結合你的兩個命題，同時擴大差異，使其可見。

接下來是試圖用ggplot2來做到這一點。其實這比我最初想象的要多一點，我對結果絕對不滿意;但也許它有幫助。評論和改進非常受歡迎。

library(ggplot2) 
library(dplyr) 

## function that replicates default ggplot2 colors 
## taken from [1] 
gg_color_hue <- function(n) { 
    hues = seq(15, 375, length=n+1) 
    hcl(h=hues, l=65, c=100)[1:n] 
} 

## Set up sample data 
set.seed(1) 
n <- 2000 
x1 <- rlnorm(n, 0, 1) 
x2 <- rlnorm(n, 0, 1.1) 
df <- bind_rows(data.frame(sample=1, x=x1), data.frame(sample=2, x=x2)) %>% 
    mutate(sample = as.factor(sample)) 

## Calculate density estimates 
g1 <- ggplot(df, aes(x=x, group=sample, colour=sample)) + 
    geom_density(data = df) + xlim(0, 10) 
gg1 <- ggplot_build(g1) 

## Use these estimates (available at the same x coordinates!) for 
## calculating the differences. 
## Inspired by [2] 
x <- gg1$data[[1]]$x[gg1$data[[1]]$group == 1] 
y1 <- gg1$data[[1]]$y[gg1$data[[1]]$group == 1] 
y2 <- gg1$data[[1]]$y[gg1$data[[1]]$group == 2] 
df2 <- data.frame(x = x, ymin = pmin(y1, y2), ymax = pmax(y1, y2), 
        side=(y1<y2), ydiff = y2-y1) 
g2 <- ggplot(df2) + 
    geom_ribbon(aes(x = x, ymin = ymin, ymax = ymax, fill = side, alpha = 0.5)) + 
    geom_line(aes(x = x, y = 5 * abs(ydiff), colour = side)) + 
    geom_area(aes(x = x, y = 5 * abs(ydiff), fill = side, alpha = 0.4)) 
g3 <- g2 + 
    geom_density(data = df, size = 1, aes(x = x, group = sample, colour = sample)) + 
    xlim(0, 10) + 
    guides(alpha = FALSE, colour = FALSE) + 
    ylab("Curves: density\n Shaded area: 5 * difference of densities") + 
    scale_fill_manual(name = "samples", labels = 1:2, values = gg_color_hue(2)) + 
    scale_colour_manual(limits = list(1, 2, FALSE, TRUE), values = rep(gg_color_hue(2), 2)) 

print(g3) 

來源：SO answer 1，SO answer 2

---

正如意見建議的@Gregor，這裏有一個版本，那麼下面的海誓山盟兩個獨立的地塊，但共享相同x軸縮放。至少傳說應該明顯地被調整。

library(ggplot2) 
library(dplyr) 
library(grid) 

## function that replicates default ggplot2 colors 
## taken from [1] 
gg_color_hue <- function(n) { 
    hues = seq(15, 375, length=n+1) 
    hcl(h=hues, l=65, c=100)[1:n] 
} 

## Set up sample data 
set.seed(1) 
n <- 2000 
x1 <- rlnorm(n, 0, 1) 
x2 <- rlnorm(n, 0, 1.1) 
df <- bind_rows(data.frame(sample=1, x=x1), data.frame(sample=2, x=x2)) %>% 
    mutate(sample = as.factor(sample)) 

## Calculate density estimates 
g1 <- ggplot(df, aes(x=x, group=sample, colour=sample)) + 
    geom_density(data = df) + xlim(0, 10) 
gg1 <- ggplot_build(g1) 

## Use these estimates (available at the same x coordinates!) for 
## calculating the differences. 
## Inspired by [2] 
x <- gg1$data[[1]]$x[gg1$data[[1]]$group == 1] 
y1 <- gg1$data[[1]]$y[gg1$data[[1]]$group == 1] 
y2 <- gg1$data[[1]]$y[gg1$data[[1]]$group == 2] 
df2 <- data.frame(x = x, ymin = pmin(y1, y2), ymax = pmax(y1, y2), 
        side=(y1<y2), ydiff = y2-y1) 
g2 <- ggplot(df2) + 
    geom_ribbon(aes(x = x, ymin = ymin, ymax = ymax, fill = side, alpha = 0.5)) + 
    geom_density(data = df, size = 1, aes(x = x, group = sample, colour = sample)) + 
    xlim(0, 10) + 
    guides(alpha = FALSE, fill = FALSE) 
g3 <- ggplot(df2) + 
    geom_line(aes(x = x, y = abs(ydiff), colour = side)) + 
    geom_area(aes(x = x, y = abs(ydiff), fill = side, alpha = 0.4)) + 
    guides(alpha = FALSE, fill = FALSE) 
## See [3] 
grid.draw(rbind(ggplotGrob(g2), ggplotGrob(g3), size="last")) 

...或abs(ydiff)通過ydiff在第二情節的建設代替：

來源：SO answer 3