Why do they call the power law distribution a 'law' Power law distribution is a distribution not a law. Very simple question: why is it called a law?
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Why do they call the power law distribution a 'law'

In the specific case of "power law" the term "power law" is a term in science. It refers to a connection between two phenomena that have a relationship that goes as a power, $y \propto x^\alpha$.
e.g. see this page (from Harvey Mudd College's physics dept) on Power Law:

When one quantity (say y) depends on another (say x) raised to some power, we say that y is described by a power law.

Also see the Wikipedia article on Power law
That sense of law similar to the use of the word for many other physical laws.
This descriptor ("power law") is often applied when it's the probability density of some quantity (or in discrete cases, the pmf) that has that property, $f(x) \propto x^\alpha$; whence "power law distribution".
These "power law" phenomena crop up a lot ... though perhaps not nearly as often as they're claimed. See A. Clauset, C.R. Shalizi, and M.E.J. Newman (2009), "Power-law distributions in empirical data" SIAM Review 51(4), 661-703
(arxiv here) and Shalizi's So You Think You Have a Power Law — Well Isn't That Special? (see here).

Power law distribution is a distribution not a law.

Here the term "law" goes with "power" (the distribution whose density follows a "power-law") rather than distribution, but actually, in statistics, the term "law" was frequently used (and to a lesser extent, still is) simply as a term for distribution.
This is closely related to the meaning of the term "law" in science (the effect that some particular phenomenon always occurs if specific conditions hold). [There's also likely some connection to the use of the word law in mathematics, as a kind of mathematical rule.]
So for example, under certain conditions, you'd expect quantities to have something like a normal distribution (measured quantities with lots of small errors adding together, the conditions for the "normal law"), and under other conditions you'd expect quantities to have something like a Poisson distribution (counting rare events happening at constant rate, independently, the conditions for the "Poisson law")
So you can readily find references to "normal law", "Poisson law" (sometimes "the law of small numbers" or "the law of rare events") and so on.
e.g.

*

*see the end of this section of the Wikipedia article on the normal distribution:


*

*Pearson distribution— a four-parametric family of probability distributions that extend the normal law to include different skewness and kurtosis values.




*In the Notes section of the Wikipedia article on the Poisson distribution:



*Raikov, D. (1937). On the decomposition of Poisson laws. Comptes Rendus (Doklady) de l' Academie des Sciences de l'URSS, 14, 9–11. (The proof is also given in von Mises, Richard (1964). Mathematical Theory of Probability and Statistics. New York: Academic Press.)




*Same article, see the end of this section:

The word law is sometimes used as a synonym of probability distribution, and convergence in law means convergence in distribution. Accordingly, the Poisson distribution is sometimes called the law of small numbers because it is the probability distribution of the number of occurrences of an event that happens rarely but has very many opportunities to happen.

(emphases mine)
So "law" can mean "distribution", but in the phrase "power law distribution" it doesn't, since "distribution" already takes that role (as mentioned earlier, it's the distribution that has a "power-law" in the scientific sense). However, when the phrase "power law" without the word "distribution" is nevertheless referring to a distribution, it can be taken to carry that meaning, as for example, in the title of Shalizi's blog item above "So You Think You Have a Power Law" (clearly one wouldn't say "Power-law Law" in that case, since the first "law" can convey the entire sense on its own).
A: As whuber et al. state, this is just a naming convention. Not actually a law per se. One could easily be confused in the sense that they may think that this is a law like Newton's law.
