There's a paper by B. Mandelbrot and N. Taleb Mild vs Wild Randomness that says that Pareto distributions is a better fit for modelling price changes.

P(X>x) = Kx^-α
where P(X>x) is the probability of exceeding a variable x
and α is the asymptotic power law exponent for x large enough

α ~ 3 for stocks

Is there a more detailed, practical example how it can be used? To estimate price distribution from historical prices? Ideally with some scripts in Python, R, Java etc.

  • 1
    $\begingroup$ You need to look at maximum likelihood for fitting a power law distribution - sadly, this is non trivial due to the xmin xmax variables which are themselves troublesome to derrive, en.wikipedia.org/wiki/Power_law#Maximum_likelihood $\endgroup$
    – wildbunny
    Dec 7, 2019 at 18:26


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