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I want to create a plot that overlays a heavy vs light tailed distribution as an example and am trying to figure out the best way to do this.

I can plot gamma distribution which is light tailed and a pareto, which is heavy but they are inherently different. As such, they are somewhat hard to compare? Any suggestions of what two distributions make a good picture?

Thanks!

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    $\begingroup$ When you say 'distribution' do you mean density-function or distribution-function? $\endgroup$
    – Glen_b
    Commented Aug 10, 2014 at 23:40
  • $\begingroup$ I think that @whuber's answer here could also be of help. $\endgroup$
    – COOLSerdash
    Commented Aug 12, 2014 at 16:37

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Log-log plot is your best choice. Here's an image of mine from this tutorial. Top is linear scale for both, and bottom image is log-log. Notice how the tails are indistinguishable in the linear plot but very clearly different in the log-log plot.

From tutorial

As for R, the following web page describes how to set ggplot2 to use log-log scales: http://docs.ggplot2.org/current/scale_continuous.html

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I think you are asking for 2 different distributions that share some common 'essence', but that differ in how heavy their tails are, so that when you plot them the nature of 'heavy-tailedness' can be demonstrated. Is that correct? If so, why not use the $t$ distribution with $1$ and $\infty$ degrees of freedom? Here is a plot of several $t$ distributions from the Wikipedia page:

enter image description here

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