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I have come across a picture of a density plot that I understand visually and conceptually but I am confused by the terminology. It is referred to as simply a "Density Plot". Have a look:

enter image description here

Question: If a researcher refers to a graph as a density plot, what does he/she probably mean?

Unfortunately I couldn't find the URL to accompany the picture, so we won't be able to examine everything under the hood. However, I'm hoping someone can tell what it most likely is just by glancing at it, or at least weigh in on what the conventional understanding of "Density Plot" implies.

If I'm not mistaken there are many types of densities plots. If I had to guess, judging by the smoothness, it is a kernel distribution of some sort. I did a bit of research and found out there are many types of kernel distributions: Epanechnikov, uniform, triangular, biweight, normal, and cosinus just to name a few.

Since there are so many out there, I'm wondering if we wouldn't have to specify which type of density is being plotted? Or is one type much more common than the other types, to the effect that "Density Plot" is assumed to mean that type and not any other type unless otherwise stated?

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"Density", or the probability density function, is a basic concept that is above the specific estimation of a density curve. A more comprehensive reference can be found in many textbooks or even here https://en.wikipedia.org/wiki/Probability_density_function. Roughly, the density plots above appear to reflect an empiricial estimation of the relative likelihood that a given sample has the specified value on the x-axis.

Once you understand this, then there are a variety of methods to estimate the density for a random variable given the limited sample you have, as you already have listed some in your post.

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  • $\begingroup$ Thank you, I get that much for the most part. As far as methods to estimate densities go, is there a standard one? The graph in my post didn't specify which method was used for estimation. I have two theories on that. 1. There is a standard density estimation method, and as such the method was omitted. 2. Most graphs do specify the density estimation method, meaning that my picture is an exception. I don't know, maybe there is more to it. $\endgroup$ – Arash Howaida Feb 10 '18 at 18:57
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    $\begingroup$ I better see what you mean now. Ideally, you would have this information with the graph. This is a biased view, but in my field, most people do not put this information with density graphs. Usually you can find it in the methods section. If this is missing, I try to guess what was done by how the graph looks. Here, this graphs looks like it came from ggplot which is an R package, so I would guess this was generated using the density() function with default parameters. But I cannot be certain, of course. $\endgroup$ – Daniel Feb 10 '18 at 19:09
  • $\begingroup$ Ok cool, that helps. I don't know too much about R, but just out of curiosity, what is the default setting for density estimation method for R's density() ? Like you said, we can't be certain, but perhaps R's default setting here and my search for the conventional terminology are one and the same. $\endgroup$ – Arash Howaida Feb 10 '18 at 19:41
  • $\begingroup$ You can find more details here: stat.ethz.ch/R-manual/R-devel/library/stats/html/density.html. But by default, density() uses a Gaussian kernel. $\endgroup$ – Daniel Feb 10 '18 at 19:46
  • $\begingroup$ Interesting, R's default is Gaussian, which I presume to be synonymous with "normal" in my OP. I check my statistics software's default kernel and it turned out to be Epanechnikov. I wonder which of the two is most common. $\endgroup$ – Arash Howaida Feb 10 '18 at 19:50

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