将正态曲线叠加到R中的直方图

Question

我已经设法在网上找到如何将正常曲线叠加到 R 中的直方图上，但我想保留直方图的正常“频率”y 轴。请参阅下面的两个代码段，并注意在第二个代码段中，y 轴如何替换为“密度”。我怎样才能将 y 轴保持为“频率”，就像在第一个图中一样。

作为奖励：我还想在密度曲线上标记 SD 区域（最多 3 个 SD）。我怎样才能做到这一点？我试过abline，但这条线延伸到图的顶部，看起来很丑。

g = d$mydata
hist(g)

g = d$mydata
m<-mean(g)
std<-sqrt(var(g))
hist(g, density=20, breaks=20, prob=TRUE, 
     xlab="x-variable", ylim=c(0, 2), 
     main="normal curve over histogram")
curve(dnorm(x, mean=m, sd=std), 
      col="darkblue", lwd=2, add=TRUE, yaxt="n")

在上图中，y 轴是“密度”。我想让它成为“频率”。

Answer 1

您需要找到正确的乘数来将密度（曲线下方面积为 1 的估计曲线）转换为计数。这可以很容易地从hist 对象中计算出来。

myhist <- hist(mtcars$mpg)
multiplier <- myhist$counts / myhist$density
mydensity <- density(mtcars$mpg)
mydensity$y <- mydensity$y * multiplier[1]

plot(myhist)
lines(mydensity)

一个更完整的版本，具有正态密度和远离平均值（包括平均值）的每个标准差处的线条：

myhist <- hist(mtcars$mpg)
multiplier <- myhist$counts / myhist$density
mydensity <- density(mtcars$mpg)
mydensity$y <- mydensity$y * multiplier[1]

plot(myhist)
lines(mydensity)

myx <- seq(min(mtcars$mpg), max(mtcars$mpg), length.out= 100)
mymean <- mean(mtcars$mpg)
mysd <- sd(mtcars$mpg)

normal <- dnorm(x = myx, mean = mymean, sd = mysd)
lines(myx, normal * multiplier[1], col = "blue", lwd = 2)

sd_x <- seq(mymean - 3 * mysd, mymean + 3 * mysd, by = mysd)
sd_y <- dnorm(x = sd_x, mean = mymean, sd = mysd) * multiplier[1]

segments(x0 = sd_x, y0= 0, x1 = sd_x, y1 = sd_y, col = "firebrick4", lwd = 2)

Answer 2

只需删除prob = T，让它保持默认即F

Answer 3

这是前面提到的StanLe's anwer 的实现，也解决了他的答案在使用密度时不会产生曲线的情况。

这将替换现有但隐藏的hist.default() 函数，只添加normalcurve 参数（默认为TRUE）。

前三行是为了支持roxygen2进行包构建。

#' @noRd
#' @exportMethod hist.default
#' @export
hist.default <- function(x,
                         breaks = "Sturges",
                         freq = NULL,
                         include.lowest = TRUE,
                         normalcurve = TRUE,
                         right = TRUE,
                         density = NULL,
                         angle = 45,
                         col = NULL,
                         border = NULL,
                         main = paste("Histogram of", xname),
                         ylim = NULL,
                         xlab = xname,
                         ylab = NULL,
                         axes = TRUE,
                         plot = TRUE,
                         labels = FALSE,
                         warn.unused = TRUE,
                         ...)  {

  # https://*.com/a/20078645/4575331
  xname <- paste(deparse(substitute(x), 500), collapse = "\n")

  suppressWarnings(
    h <- graphics::hist.default(
      x = x,
      breaks = breaks,
      freq = freq,
      include.lowest = include.lowest,
      right = right,
      density = density,
      angle = angle,
      col = col,
      border = border,
      main = main,
      ylim = ylim,
      xlab = xlab,
      ylab = ylab,
      axes = axes,
      plot = plot,
      labels = labels,
      warn.unused = warn.unused,
      ...
    )
  )

  if (normalcurve == TRUE & plot == TRUE) {
    x <- x[!is.na(x)]
    xfit <- seq(min(x), max(x), length = 40)
    yfit <- dnorm(xfit, mean = mean(x), sd = sd(x))
    if (isTRUE(freq) | (is.null(freq) & is.null(density))) {
      yfit <- yfit * diff(h$mids[1:2]) * length(x)
    }
    lines(xfit, yfit, col = "black", lwd = 2)
  }

  if (plot == TRUE) {
    invisible(h)
  } else {
    h
  }
}

快速示例：

hist(g)

日期有点不同。供参考：

#' @noRd
#' @exportMethod hist.Date
#' @export
hist.Date <- function(x,
                      breaks = "months",
                      format = "%b",
                      normalcurve = TRUE,
                      xlab = xname,
                      plot = TRUE,
                      freq = NULL,
                      density = NULL,
                      start.on.monday = TRUE,
                      right = TRUE,
                      ...)  {

  # https://*.com/a/20078645/4575331
  xname <- paste(deparse(substitute(x), 500), collapse = "\n")

  suppressWarnings(
    h <- graphics:::hist.Date(
      x = x,
      breaks = breaks,
      format = format,
      freq = freq,
      density = density,
      start.on.monday = start.on.monday,
      right = right,
      xlab = xlab,
      plot = plot,
      ...
    )
  )

  if (normalcurve == TRUE & plot == TRUE) {
    x <- x[!is.na(x)]
    xfit <- seq(min(x), max(x), length = 40)
    yfit <- dnorm(xfit, mean = mean(x), sd = sd(x))
    if (isTRUE(freq) | (is.null(freq) & is.null(density))) {
      yfit <- as.double(yfit) * diff(h$mids[1:2]) * length(x)
    }
    lines(xfit, yfit, col = "black", lwd = 2)
  }

  if (plot == TRUE) {
    invisible(h)
  } else {
    h
  }
}

Answer 4

这是我找到的一个不错的简单方法：

h <- hist(g, breaks = 10, density = 10,
          col = "lightgray", xlab = "Accuracy", main = "Overall") 
xfit <- seq(min(g), max(g), length = 40) 
yfit <- dnorm(xfit, mean = mean(g), sd = sd(g)) 
yfit <- yfit * diff(h$mids[1:2]) * length(g) 

lines(xfit, yfit, col = "black", lwd = 2)