Intuition behind power law distribution

I know that the pdf of a power law distribution is p(x)=α1xmin(xxmin)α

But what does it intuitively mean if, for example, stock prices follow a power law distribution? Does this mean that losses can be very high but infrequent?


This is an heavy tailed distribution, since the cdf is
So the probability to exceed x, (x/x_\min)^{1-\alpha} can be made arbitrarily close to 1 by the proper choice of \alpha. For instance, if one wants the probability to exceed 10^u x_\min to be at least 0.9, one should pick \alpha to be at most


a curve represented below, with the first axis being scaled by u, not by 10^u x_\min
R curve rendering of the above function

Source : Link , Question Author : Thomas James , Answer Author : Xi’an

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