Exponential binning

  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.

  2. jcsd
  3. mathman

    mathman 6,750
    Science Advisor
    Gold Member

    Use semilog graph paper.
  4. Mute

    Mute 1,390
    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. Thanks indeed!
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