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I am not really sure how to even phrase this question, but here it goes:

I'm looking at a distribution that follows a power curve (I think).. it looks something like this:

f(0):  100000
f(1):   10000
f(10):   1000
f(100):   100
f(1000):   10
f(10000):   1
f(100000): .1
  1. Is this a power curve?

  2. Am I to take it that for all power curves, that $x \cdot f(x)$, and also $\log(x) + \log(f(x))$ is constant, or is this a special case?

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1 Answer 1

up vote 0 down vote accepted

Aside from $f(0)$ they follow $f(x)=\frac {10000}x$ perfectly. This is a power curve with exponent $-1$

For 2, $x \cdot f(x)$ is only constant if the exponent is $-1$. $\log x + \log f(x) = \log (x \cdot f(x))$ so this will be constant again when the exponent is $-1$

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How is it that power curves can have the 80-20 effect if they are divergent? –  math_idiot Feb 10 '13 at 4:32
    
@math_idiot: There are several things mixed up in that question. Divergence talks about what happens "at infinity". Real world power laws don't go that far, though they can be power laws far enough to be useful, so whether they diverge is not that important. The 80-20 rule is a rough rule of thumb that doesn't automatically arise from a power law-the uniform distribution is a power law (with exponent zero) and doesn't support it. –  Ross Millikan Feb 10 '13 at 16:39

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