alt Hacker NewsI don't understand how this is a power law and not normal. The "long tail" is usually mentioned in a normal distribution being the right-most end of it.
I don't understand how this is a power law and not normal. The "long tail" is usually mentioned in a normal distribution being the right-most end of it.
I think you have a misunderstanding because a heavy tail is essentially one that is not exponentially bounded. A long tail being a subclass.
There's kinda a big difference in the characteristics of a normal distribution and power and I think explaining that will really help.
In a normal you have pressure from both ends so that's why you find it in things like height. There's evolutionary pressure to not be too small but also pressure to not be too large. Being tall is advantageous but costly. Technically the distribution never ends (and that's in either direction!). Though you're not going to see micro people nor 100' tall people because the physics gets in the way. Also mind you that normal can't be less than zero.
It is weird to talk about "long tail" with normal distributions and flags should go up when hearing this.
In a power distribution you don't have bounding pressure. So they are scale free. A classic example of this is wealth. It's easier to understand if you ignore the negative case at first, so let's do that (it still works with negative wealth). There's no upper bound to wealth, right? So while most people will be in the main "mode" there is a long tail. We might also say something like "heavy tail" when the variance is even moderate. So this tail is both long and the median value isn't really representative of the distribution. Funny enough, power laws are incredibly common in nature. I'm really not sure why they aren't discussed more.
I think Veritasium did a video on power distributions recently? Might be worth a check.
Heavy tail: https://en.wikipedia.org/wiki/Heavy-tailed_distribution
Long tail: https://en.wikipedia.org/wiki/Long_tail