I have long struggled to bring kernel density plots into the "mainstream." See Reading kernel distribution plot vs typical histogram. However, I recently came across a report that pulled off the tricky inference vs aesthetics trade-off that can be too one-sided with these types of visuals:

enter image description here

  • It has smooth curvature, something we tend to find in kernel density plots
  • However, it has a y axis in absolutes, not the decimal intervals we use for taking the interval between two points on the kernel density plot

This leads me to believe it's not a kernel density plot but simply a line representation of the spread.


If this is not a kernel density, what is this chart and how is the line curvature calculated? There appears to be non-linear mechanics, not just throwing the data in a line wrapper.
  • $\begingroup$ There is no reference here. If the original report did not say how the smooth curves were produced, it is hard for us to say more. In particular, most kernel density estimation routines would smooth some probability mass below the minimum and above the maximum, not what is shown. In short, what has been done is a mystery, beyond the question of whether smoothing is needed, valid and helpful. $\endgroup$
    – Nick Cox
    Jun 17, 2021 at 7:52

1 Answer 1

  • Not every probability density function is a kernel density. Form the image alone we cannot guess what exactly is it. It could be KDE, but could be a parametric distribution as well.
  • To align heights of histogram and density function, you just need to multiply the probability densities by a constant. They would lose the numerical meaning, since would not integrate to one anymore, but would look better on a plot. This is a common practice.
  • $\begingroup$ Was not aware of this solution. It is starting to make sense though, thanks $\endgroup$ Jun 17, 2021 at 5:49
  • 2
    $\begingroup$ Some people talk of frequency density. The curve then integrates, or should integrate, to total frequency, $\endgroup$
    – Nick Cox
    Jun 17, 2021 at 7:54

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