The Pareto Distribution

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As far as I understand it, and for those unaware, the Pareto Distribution is a theory of probability that posits the base claim that the square root of a population receives half of any distributable item.

It’s sometimes referred to as the 80-20 rule (90-10?). It was originally used to give reason to income inequity and wealth distribution but has been observed throughout our reality.

From Wikipedia, this theory can be seen in file size distribution of internet traffic, the failure rate of hard drives, sizes of sand particles, Tinder (80% of females compete for the top 20% of the most attractive males), the amount of time people play their games on Steam (a few games get played a ton, most never get played).

I can’t even read all of those logarithmic type equations and functions on the page. It flies right over my head, so if someone can simplify those I would appreciate it.

What I also need help understanding is why or how this is even an observable phenomenon. Is it something that is simply a natural law, like gravity? If so, how does it happen so consistently? Or is it something we actively attempt to achieve as humans (as it relates to tangible, actionable things like wealth as opposed to natural things like sand particles)? If so, why do we do this?

In: Mathematics

Anonymous 0 Comments

The Pareto distribution isn’t really a theory, it’s just a bit of math that describes what happens if you have some random variable (file size on internet traffic, size of sand particles, etc.) that follows a power law. “Power Law” just means it follows some quantity raised to a power (like squared or cubed), not linear.

A *lot* of natural phenomenon can be described, or at least approximated, by a power law. With the right parameters, you can use it to model an awful lot of stuff, hence versions of the Pareto distribution will show up in a lot of places.

Intuitively, thing about anything that is bounded on one side, doesn’t have a functional maximum, and where the amount of stuff you get in the future depends on how much you have right now. Like sand grains…you can’t have a sand grain of size zero or negative (then it wouldn’t be a sand grain), so it’s bounded on one size. You can’t really have a maximum size sand grain (we call that a boulder, which is functionally “infinitely big sand grain”). And small sand is produced by grinding down bigger sand, and it’s easier to break small grains than big ones, so the number of sand grains produced scales up with the amount of sand we already have and we get faster generation of small ones than big ones (that last piece is the power law part kicking in).

So the Pareto distribution itself isn’t a physical law, like gravity, but it is a good math model for what happens when a number of physical laws play out in the universe.