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Math Help - Plots & Distributions

  1. #1
    Junior Member
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    Plots & Distributions

    I seek advise on the following comment:

    "Observing the log-log plot we can see that degree distribution fits well to a power law distribution."

    The author of the comment proposes that the nature of the distribution only becomes ostensible if seen at log scale.

    My question is the following:

    What would prompt a conductor of a given study to investigate functions of the X- & Y- axis variables? Do certain specific properties of the data encourage further investigation? If yes, which functions other than log should be considered?

    Would greatly appreciate advise.

    Best,
    wirefree
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  2. #2
    MHF Contributor
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    Thumbs up Log-log plots

    Hello wirefree
    Quote Originally Posted by wirefree View Post
    I seek advise on the following comment:

    "Observing the log-log plot we can see that degree distribution fits well to a power law distribution."

    The author of the comment proposes that the nature of the distribution only becomes ostensible if seen at log scale.

    My question is the following:

    What would prompt a conductor of a given study to investigate functions of the X- & Y- axis variables? Do certain specific properties of the data encourage further investigation?
    A very brief answer would be that a log-log plot is useful if you think you may have a function of the form

    f(x) = ax^n

    and you want to find out (a) whether this is so; (b) if so, the values of a and n.

    If we take logs of both sides:

    \log(f(x)) = \log(ax^n)

    = \log(a) + n \log(x), using the laws of logarithms.

    Thus, if the function is of the form f(x) = ax^n, the log-log plot will produce a straight line graph, whose gradient gives the value of n, and intercept the value of \log(a). (So if the base of the logarithm is 10, and the intercept is c, the value of a is given by a = 10^c.)

    Other applications include the investigation of functions that are themselves logarithmic in nature - the bel and decibel for the measurement of acoustic power, for example.

    Here's the Wikipedia article (which perhaps you've already looked at!): Logarithmic scale - Wikipedia, the free encyclopedia.

    If yes, which functions other than log should be considered?
    I can't think of any others that would be useful!

    I hope that helps to shed a little light.

    Grandad
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