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The Pareto distribution is defined from the CDF: $$ F^{-1}(p) = \frac{b}{(1 − p)^{1/a}},\ 0 < p < 1, $$ where, $b$ is the scale parameter and $a$ is the shape parameter.

In the Gaussian case, in order to detect if there is variability in the samples, the variability index is defined as fellows:
$$ VI = 1 + \frac{{\rm var}(X)}{{\rm mean}(X)^2} $$ Is the definition of $VI$ still maintained with Pareto samples (given the very spiky character, long tail, etc. of the Pareto distribution)?

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  • $\begingroup$ en.wikipedia.org/wiki/Pareto_distribution tells you the mean and the variance, which you can plug into the formula for $VI$. If that doesn't fully answer your question, could you explain what you mean by "maintaining" a definition? $\endgroup$ – whuber Apr 25 '16 at 21:47
  • $\begingroup$ the variability is used to detect if there are spurious data added with the original samples, with the gaussian case VI as described works fine; but in non-gaussian case , samples are very spiky , the VI can detect variability even there are not. I want to now if there is other tools rather than VI when we use Pareto to fit data and detect variability? $\endgroup$ – user113486 Apr 29 '16 at 9:10

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