Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

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!

share|improve this question
1  
When you say 'distribution' do you mean density-function or distribution-function? –  Glen_b Aug 10 at 23:40
    
I think that @whuber's answer here could also be of help. –  COOLSerdash Aug 12 at 16:37

2 Answers 2

up vote 5 down vote accepted

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

share|improve this answer

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

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.