密度图下的面积不等于1 [英] Area under a density plot not equal to 1

问题描述

我试图用ggplot来绘制概率密度图。我的问题是曲线下的面积不等于一个。建议表示赞赏。

示例图表...生成此图表的代码如下所示... Y轴看起来像是一个小尺寸垃圾箱的计数，而不是落入该垃圾箱的概率。示例代码但是，如果您习惯于盯着PDF并将其总和，那么对数据进行规范化将为您提供更直观的情节为1.但不要误解y轴。 y不是从密度等于x的随机抽取值的概率。

I am trying to chart a probability density plot using ggplot. My problem is that the area under the curve is not equal to one. Advice appreciated.

Sample chart... the code that produced this chart follows... The Y axis looks like it is a count for small sized bins, rather than a probability for falling into that bin. The example code here, is one of the sources I drew on in the preparation of this chart.

Sample code... most of which is data... the key bit of code is at the bottom...

library(ggplot2)
library(reshape)
library(plyr)
library(scales)

Date <- as.Date(
    c("1976-01-16", "1976-02-15", "1976-03-16", "1976-04-15", "1976-05-16",
      "1976-06-15", "1976-07-16", "1976-08-16", "1976-09-15", "1976-10-16",
      "1976-11-15", "1976-12-16", "1977-01-16", "1977-02-14", "1977-03-16",
      "1977-04-15", "1977-05-16", "1977-06-15", "1977-07-16", "1977-08-16",
      "1977-09-15", "1977-10-16", "1977-11-15", "1977-12-16", "1978-01-16",
      "1978-02-14", "1978-03-16", "1978-04-15", "1978-05-16", "1978-06-15",
      "1978-07-16", "1978-08-16", "1978-09-15", "1978-10-16", "1978-11-15",
      "1978-12-16", "1979-01-16", "1979-02-14", "1979-03-16", "1979-04-15",
      "1979-05-16", "1979-06-15", "1979-07-16", "1979-08-16", "1979-09-15",
      "1979-10-16", "1979-11-15", "1979-12-16", "1980-01-16", "1980-02-15",
      "1980-03-16", "1980-04-15", "1980-05-16", "1980-06-15", "1980-07-16",
      "1980-08-16", "1980-09-15", "1980-10-16", "1980-11-15", "1980-12-16",
      "1981-01-16", "1981-02-14", "1981-03-16", "1981-04-15", "1981-05-16",
      "1981-06-15", "1981-07-16", "1981-08-16", "1981-09-15", "1981-10-16",
      "1981-11-15", "1981-12-16", "1982-01-16", "1982-02-14", "1982-03-16",
      "1982-04-15", "1982-05-16", "1982-06-15", "1982-07-16", "1982-08-16",
      "1982-09-15", "1982-10-16", "1982-11-15", "1982-12-16", "1983-01-16",
      "1983-02-14", "1983-03-16", "1983-04-15", "1983-05-16", "1983-06-15",
      "1983-07-16", "1983-08-16", "1983-09-15", "1983-10-16", "1983-11-15",
      "1983-12-16", "1984-01-16", "1984-02-15", "1984-03-16", "1984-04-15",
      "1984-05-16", "1984-06-15", "1984-07-16", "1984-08-16", "1984-09-15",
      "1984-10-16", "1984-11-15", "1984-12-16", "1985-01-16", "1985-02-14",
      "1985-03-16", "1985-04-15", "1985-05-16", "1985-06-15", "1985-07-16",
      "1985-08-16", "1985-09-15", "1985-10-16", "1985-11-15", "1985-12-16"))

GOLD <- c(
  -0.104,  0.051,  0.011, -0.035, -0.008, -0.010, -0.065, -0.067,  0.041,  0.017,
   0.126,  0.023, -0.011,  0.029,  0.087,  0.007, -0.016, -0.044,  0.048, -0.013,
   0.030,  0.062, -0.029,  0.042,  0.078,  0.028,  0.031, -0.045,  0.005,  0.043,
   0.028,  0.090,  0.030,  0.072, -0.094,  0.009,  0.093,  0.080, -0.014, -0.013,
   0.077,  0.084,  0.058,  0.021,  0.184,  0.097,  0.002,  0.169,  0.474, -0.014,
  -0.168, -0.067, -0.007,  0.169,  0.071, -0.025,  0.077, -0.022, -0.059, -0.044,
  -0.063, -0.103, -0.003, -0.008, -0.031, -0.040, -0.113,  0.005,  0.081, -0.014,
  -0.057, -0.009, -0.062, -0.026, -0.117,  0.061, -0.046, -0.058,  0.080,  0.076,
   0.190, -0.031, -0.019,  0.074,  0.079,  0.022, -0.144,  0.030,  0.013, -0.057,
   0.026, -0.017, -0.012, -0.042, -0.030,  0.015, -0.043,  0.041,  0.022, -0.032,
  -0.011,  0.001, -0.083,  0.004, -0.019, -0.002,  0.003, -0.065, -0.063,  0.017,
  -0.044,  0.134, -0.022, -0.014, -0.008,  0.033, -0.014,  0.017, -0.004, -0.023)

df <- data.frame(Date=Date, GOLD=GOLD)

p <- ggplot(data=df, aes(x=GOLD, y=..density..)) +
    stat_density(fill='grey50') +
    xlab('Percent change on previous month') +
    ylab('Density') +
    opts(title='Change in Gold Price in the US')
ggsave(p, width=8, height=4, filename='plot.png', dpi=125)

解决方案

I don't think this is a problem with ggplot, but with your understanding of the y-axis in a density plot. The base plotting functions in R plot the same thing. You can set the call to y=..scaled.. to give you a relative density, but if you use stat_bin() you'll see the actual histogram and notice it's not the counts. If you want you could normalize your data with something like this:

GOLD_N <- (GOLD- mean(GOLD))/sd(GOLD)
df <- data.frame(Date=Date, GOLD=GOLD,GOLD_N=GOLD_N)

Then run your plot it will look something like this:

You should watch this video about how to interpret density functions http://www.youtube.com/watch?v=Fvi9A_tEmXQ But normalizing your data will give you the plot that's a bit more intuitive if you're used to staring at PDF's and will sum to 1. But don't misinterpret the y axis. y IS NOT the probability of a randomly drawn value from the density being equal to x.

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