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Power Law Distribution

  1. Oct 14, 2013 #1
    Hi All,

    After reading some books on how stock market returns are better modelled by a power law distribution, I wanted to play with some data based on this.

    When using some software and or doing it myself on excel, I can generate one tail, but not two.

    This is what I would like my data to look like;


    Does anyone know how to do this?

    As you might have gathered, I am well out of my depth here. Just looking to tinker with the data for fun.
  2. jcsd
  3. Oct 14, 2013 #2


    Staff: Mentor

    Welcome to PF!

    Here's an article on using power laws in finance with pointers to other related articles which may be a good start:


    There are also several papers on this very topic that you can find via Google that I didn't include here because they may be too technical.

    With respect to your question though: Can you describe what you mean by one tail vs two tails? is this a limitation of your data or the choice of parameters for your power law graph?
  4. Oct 14, 2013 #3
    Thanks for the quick reply.
    That article is exactly what I am trying to do.

    What I meant by one tail is I can calculate say a graph like this for the positive returns;


    But I am not sure of the formula I need to use to get the overall distribution or bell shape.

    Even better, if this is called a particular distribution I would prefer to generate the graph in a software package. I downloaded Easyfit 5.5, but the power law distribution produces what I am describing as a "one tail" distribution such as the image above and not like the image in my original post.

    Thanks :)
  5. Oct 14, 2013 #4


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    Homework Helper

    Excel is the worst tool available for anything statistical. You could try "R" - a powerful yet free statistical software package. I believe (based on memory from a year or so ago) that there is even a package for R that will aid in generating the type of distribution you want.
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