How to best plot a heavy vs light tailed distribution in R

Question

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!

When you say 'distribution' do you mean density-function or distribution-function? — Glen_b, Aug 10 '14 at 23:40
I think that @whuber's answer [here](http://stats.stackexchange.com/a/86503/21054) could also be of help. — COOLSerdash, Aug 12 '14 at 16:37

MrMeritology · Accepted Answer · 2014-08-10T23:51:25.450

7

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

edited Aug 10 '14 at 23:51

answered Aug 10 '14 at 23:03

MrMeritology

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score 3 · Answer 2 · answered Aug 10 '14 at 23:59

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

How to best plot a heavy vs light tailed distribution in R

2 Answers2