As others have pointed out, power laws are more "normal" than the normal distribution. The reason for this is that if you have the sum independent identically

As others have pointed out, power laws are more "normal" than the normal distribution. The reason for this is that if you have the sum independent identically distributed (I.I.D.) random variables (R.V.s), if they converge to a distribution, that distribution is Levy Stable [1], which is power law in it's tails. The Gaussian is a special case in the family of Levy Stable distributions. The article states that "the sum of many independent, additive effects is approximately normally distributed" which is patently false. The sum of many independent random variables with finite variance is normally distributed. Once you relax the finite variance (and in more extreme cases, finite mean) power laws result. There are other ways to generate power laws, including having killed exponential processes [2]. There are many other references that talk about the rediscovery of power laws [3] and give many ways to "naturally" create power laws [3] [4] [5]. The article claims that multiplicative processes lead to log normal distributions. I've heard that this is actually false but unfortunately I don't have enough familiarity to see how this is not true. If anyone has more insight into this I would appreciate a link to an article or other explanation. [1] https://en.wikipedia.org/wiki/Stable_distribution https://en.wikipedia.org/wiki/Stable_distribution [2] http://www.angelfire.com/nv/telka/transfer/powerlaw_expl.pdf http://www.angelfire.com/nv/telka/transfer/powerlaw_expl.pdf [3] https://arxiv.org/pdf/physics/0601192v3.pdf https://arxiv.org/pdf/physics/0601192v3.pdf [4] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122.3769&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122... [5] http://www.angelfire.com/nv/telka/transfer/powerlaw_expl.pdf http://www.angelfire.com/nv/telka/transfer/powerlaw_expl.pdf