如何在R中绘制半柯西、马蹄、拉普拉斯、正态分布并得到指定对比效果

需要在R中绘制半柯西（Half Cauchy）、马蹄（Horseshoe）、拉普拉斯（Laplace）、正态（Normal）四种随机变量的分布对比图，原有代码运行结果不符合预期，原有代码如下：

compare_priors <- function(scale = 1, df_t = 2, xlim = c(-6, 6),ylim=c(0,50)) {
  dt_loc_scale <- function(x, df, location, scale) {
    1/scale * dt((x - location)/scale, df)
  }
  dlaplace <- function(x, location, scale) {
    0.5 / scale * exp(-abs(x - location) / scale)
  }
  dhos<-function (x, location, scale, log = FALSE){
      dens <- dnorm(x, 0, location * 25, log = log) 
  }
  stat_dist <- function(dist, ...) {
    ggplot2::stat_function(ggplot2::aes_(color = dist), ...)
  }
  ggplot2::ggplot(data.frame(x = xlim), ggplot2::aes(x)) +
    stat_dist("normal", size = 0.8, fun = dnorm,
              args = list(mean = 0, sd = scale)) +
    stat_dist("student_t", size = 0.8, fun = dt_loc_scale,
              args = list(df = df_t, location = 0, scale = scale)) +
    stat_dist("cauchy", size = 0.8, linetype = 2, fun = dcauchy,
              args = list(location = 0, scale = scale)) +
    stat_dist("laplace", size = 0.8, linetype = 2, fun = dlaplace,
              args = list(location = 0, scale = scale))+
    stat_dist("horseshoe", size = 0.8, linetype = 2, fun = dhos,
              args = list(location = 0, scale = scale)) 
}
# Cauchy has fattest tails, followed by student_t, laplace, and normal
compare_priors()

• 缺失半柯西分布的实现，原有代码仅绘制了全区间的柯西分布，半柯西仅在x≥0时有值，密度为全柯西的2倍
• 马蹄分布的密度函数实现错误，原代码错误调用了正态分布的密度函数
• 绘图区间设置错误，目标为正半轴的半分布对比，x轴应从0开始，不需要负半轴区间
• 冗余绘制了学生t分布，目标对比图中无该分布
• 半拉普拉斯、半正态的密度未做对应调整，半分布的密度需要在x≥0时乘以2，x<0时为0

compare_priors <- function(scale = 1, xlim = c(0, 6), ylim=c(0, 1.2)) {
  # 半正态分布密度
  dhalfnorm <- function(x, sd) {
    ifelse(x < 0, 0, 2 * dnorm(x, mean = 0, sd = sd))
  }
  # 半拉普拉斯分布密度
  dhalflaplace <- function(x, location = 0, scale) {
    ifelse(x < 0, 0, 2 * 0.5 / scale * exp(-abs(x - location) / scale))
  }
  # 半柯西分布密度
  dhalfcauchy <- function(x, location = 0, scale) {
    ifelse(x < 0, 0, 2 * dcauchy(x, location = location, scale = scale))
  }
  # 马蹄分布密度（标准参数化）
  dhorseshoe <- function(x, scale = 1) {
    ifelse(x == 0, 1/(pi * scale), 
           ifelse(x < 0, 0, (1/(pi * scale)) * log(1 + 2*(scale^2)/(x^2))))
  }
  # 封装绘图层
  stat_dist <- function(dist, ...) {
    ggplot2::stat_function(ggplot2::aes(color = dist), linewidth = 0.8, ...)
  }
  ggplot2::ggplot(data.frame(x = xlim), ggplot2::aes(x)) +
    stat_dist("半正态", fun = dhalfnorm, args = list(sd = scale)) +
    stat_dist("半拉普拉斯", fun = dhalflaplace, args = list(scale = scale)) +
    stat_dist("半柯西", fun = dhalfcauchy, args = list(scale = scale), linetype = 2) +
    stat_dist("马蹄", fun = dhorseshoe, args = list(scale = scale), linetype = 2) +
    ggplot2::ylim(ylim) +
    ggplot2::labs(color = "分布类型", x = "x", y = "密度") +
    ggplot2::theme_bw()
}
# 调用函数绘图
compare_priors()

运行修正后的代码即可得到符合预期的四种半分布对比图，各分布的尾部厚重程度符合半柯西>马蹄>半拉普拉斯>半正态的特征。

内容的提问来源于stack exchange，提问作者Francesco De Vincentis