如何可视化概率分布函数之间的差异？

Question

我试着想象的分布函数两个柱状图之间的差异等方面的差异在以下两条曲线：在彼此的顶部

当差异大，你可以只绘制两条曲线和如上所述填补差异，但是当差异变得非常小时，这是麻烦的。绘制此的另一种方式，正在密谋的差异本身如下：

不过，这似乎很难读给大家看这样的图是第一次，所以我想知道：有没有用其他方式可以看到两个分布函数之间的区别？

Answer 1

我想也许这可能是一个选择，只是简单地结合你的两个命题，同时扩大差异，使其可见。

接下来是试图用ggplot2来做到这一点。其实这比我最初想象的要多一点，我对结果绝对不满意;但也许它有帮助。评论和改进非常受欢迎。

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) 

来源：SO answer 1，SO answer 2

---

正如意见建议的@Gregor，这里有一个版本，那么下面的海誓山盟两个独立的地块，但共享相同x轴缩放。至少传说应该明显地被调整。

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)通过ydiff在第二情节的建设代替：

来源：SO answer 3