Is there a standard distribution in a power law curve like this

That is unrelated to healthcare, but I think healthcare follows the following distribution:

1% of patients make up 20-25% of Spending
5% make up 50-55%
20% make up 80%

I know the 20:80 rule (pareto principle) has a lot of situations in real life where it matches the curve, 20% of actions make up 80% of results. But is there a standard power law distribution? Do other situations occur where 1% consistently produce 20-30% of results, or 5% produce 50-60%?

Math is not my strong suit.

There is an article on the distribution in Wikipedia

It gives other examples:

For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.

In load testing, it is common practice to estimate that 80% of the traffic occurs during 20% of the time

In software engineering, Lowell Arthur expressed a corollary principle: “20 percent of the code has 80 percent of the errors. Find them, fix them!”
The general power law has a parameter called alpha which can be adjusted to suit individual cases. It would be possible to calculate what value of alpha corresponds to exactly 80:20.

There is the 80/20 principle where 20% of efforts provide 80% of results. But is that part of a standard distribution that also consists of 50/5, 20/1?

There is another thread on this board about how half the country lives in 147 counties. There are about 3000 counties total in the US. US population follows the same power law curve as health care costs.

20% of people live in 1% of the counties. 50% live in 5%.


I made a math error