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Exponential binning

  1. May 15, 2013 #1
    Hi,

    I need to find out how to plot my data with exponential binning.
    To better see the exponent of f(x) = x ^ \alpha, where x and f(x) are given, I am asked to do exponential binning the data.

    Would appreciate you help.

    Yours
    Atilla
     
  2. jcsd
  3. May 15, 2013 #2

    mathman

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    Science Advisor
    Gold Member

    Use semilog graph paper.
     
  4. Jun 9, 2013 #3

    Mute

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    Homework Helper

    It seems the OP hasn't replied, but there are some important issues that need to be addressed here, so I will comment on them for any future posters who stumble across this thread.

    If you are generating histograms of something which you expect to follow a power law ##y(x) \sim x^\alpha##, you need to use logarithmic binning, not exponential binning.

    That is, you want your bins to be equally spaced on a log scale, which means you want the edge of the $k$th bin, B(k), to be given by

    $$\log_{10}(B(k)) = m \log_{10} (k) + c,$$
    where m is the slope and c is the intercept, which are determined by your bin range and your number of bins. For example, if you want 10 bins between 10-6 and 100, then ##B(0) = 10^{-6}## and ##B(10) = 10^0##, and you can solve for m and c.

    Now, this next point is extremely important: when using logarithmic binning, you must divide your y-data by the width of the bin. If you do not do this, the power of ##x^\alpha## that you measure will be wrong.

    Furthermore, when estimating power laws from data, if you need anything more than a rough estimate, a linear regression is a terrible way to find the exponent. It is very prone to systematic errors. Maximum likelihood fits are a much better method. See this preprint for a discussion of properly calculating power laws from data (as well as using hypothesis testing to see if you can rule out other behaviors like log-normal distributions).
     
  5. Jun 10, 2013 #4
    Thanks indeed!
     
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