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Pareto Distribution: " Originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a

Pareto Distribution: " Originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.[3] The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto, but the concepts are distinct, and only Pareto distributions with shape value (α) of log45 ≈ 1.16 precisely reflect it. Empirical observation has shown that this 80-20 distribution fits a wide range of cases, including natural phenomena[4] and human activities." https://en.wikipedia.org/wiki/Pareto_distribution https://en.wikipedia.org/wiki/Pareto_distribution

wittyreference 6y ago
I've never been able to develop and intuitive understanding of what sort of phenomenon should obey a Pareto distribution, as opposed to a normal or logarithmic one (which I do feel I understand.) Any nuggets of insight here on HN?
- imgabe 6y ago
  Systems with positive feedback loops tend towards power law distributions. If some success can help increase the likelihood of later success, then for participants they'll reach a level where there's a snowball effect that runs away to enormous returns. Most won't get enough to get the snowball growing. If you're a musician and you have enough fans, they'll start creating more fans as they tell people about it, large numbers of people will be going to your shows and other people will hear about you, you get on the radio, you get listed as "trending" on Spotify, etc. There's also nothing to slow it down, since once you record a song once, people can listen to it effectively infinitely more times without you having to do anything else.
- cgh 6y ago
  Many phenomena that are unbounded by physical laws follow power law distributions. Nassim Taleb uses book sales as an example: popular authors get more popular exponentially. But something physically bounded like height follows a normal distribution. To put it another way, let's say you have two randomly selected authors. Their average earnings are $1,000,000 per year. Is it more likely that they each earn roughly $1,000,000 per year, or that one earns $1,000,000+ and the other almost nothing? On the other hand, you have two women whose average height is 1.7m. Is it more likely that one woman is 30cm tall and the other is over 3m tall or that they are both roughly 1.7m?
rtx 6y ago
It breaks down for wealth distribution.

wittyreference 6y ago

I've never been able to develop and intuitive understanding of what sort of phenomenon should obey a Pareto distribution, as opposed to a normal or logarithmic one (which I do feel I understand.) Any nuggets of insight here on HN?

imgabe 6y ago
Systems with positive feedback loops tend towards power law distributions. If some success can help increase the likelihood of later success, then for participants they'll reach a level where there's a snowball effect that runs away to enormous returns. Most won't get enough to get the snowball growing. If you're a musician and you have enough fans, they'll start creating more fans as they tell people about it, large numbers of people will be going to your shows and other people will hear about you, you get on the radio, you get listed as "trending" on Spotify, etc. There's also nothing to slow it down, since once you record a song once, people can listen to it effectively infinitely more times without you having to do anything else.
cgh 6y ago
Many phenomena that are unbounded by physical laws follow power law distributions. Nassim Taleb uses book sales as an example: popular authors get more popular exponentially. But something physically bounded like height follows a normal distribution. To put it another way, let's say you have two randomly selected authors. Their average earnings are $1,000,000 per year. Is it more likely that they each earn roughly $1,000,000 per year, or that one earns $1,000,000+ and the other almost nothing? On the other hand, you have two women whose average height is 1.7m. Is it more likely that one woman is 30cm tall and the other is over 3m tall or that they are both roughly 1.7m?

rtx 6y ago

It breaks down for wealth distribution.