# [R] Comparing distributions

From: Ralf B <ralf.bierig_at_gmail.com>
Date: Wed, 23 Jun 2010 15:33:54 -0400

I am trying to do something in R and would appreciate a push into the right direction. I hope some of you experts can help.

I have two distributions obtrained from 10000 datapoints each (about 10000 datapoints each, non-normal with multi-model shape (when eye-balling densities) but other then that I know little about its distribution). When plotting the two distributions together I can see that the two densities are alike with a certain distance to each other (e.g. 50 units on the X axis). I tried to plot a simplified picture of the density plot below:

```|
|                                                         *
|                                                      *     *
|                                                   *    +   *
|                                              *     +     +  *
|                     *        +           *   +            +  *
|                 *        +*     +   *  +                   + *
|              *       +       *     +                           +*
|           *       +                                               +*
|        *       +                                                    +*
|     *      +                                                          + *
|  *      +                                                               + *
|___________________________________________________________________

```

What I would like to do is to formally test their similarity or otherwise measure it more reliably than just showing and discussing a plot. Is there a general approach other then using a Mann-Whitney test which is very strict and seems to assume a perfect match. Is there a test that takes in a certain 'band' (e.g. 50,100, 150 units on X) or are there any other similarity measures that could give me a statistic about how close these two distributions are to each other ? All I can say from eye-balling is that they seem to follow each other and it appears that one distribution is shifted by a amount from the other. Any ideas?

Ralf

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