Fernanda Viégas and Martin Wattenberg’s “Flickr Flow”
The other day (and I really mean like
the other day cuz it was quite some time ago (does the more you emphasize the other day make the other day farther back in time?)) Kyle corrected me on my probability jargon -- I said that ... something ... was a heavy-tailed distribution and he corrected me that it was in fact a long-tailed distribution. Oh, I remember what it was. We watched (most) of Anvil: The Story of Anvil and were discussing how they could make money selling CDs/mp3s on the internet but probably not have big tours, cuzza the heavy/long-tailed distribution of musical tastes. Anyways, yeah, so the "it takes all kinds" idea -- is that heavy-tailed or long-tailed?
According to
Wikipedia, that definitive source, a long-tailed distribution is a special case of a heavy-tailed distribution. A heavy-tailed distribution is any distribution whose tail(s) are not exponentially bounded, or
That is, we look really far to the side of a distribution (
x → ∞), and consider the probability that we will see a value even more extreme than this value for this distribution and for the
exponential distribution. The distribution is heavy-tailed if the probability of an extreme event is much larger for this distribution than for the exponential distribution (the ratio is ∞ as
x → ∞).
For long-tailed distributions, the requirement is more extreme:
for all
t > 0. That is, for large
x, the if you're going to see something bigger than
x, then you're going to see something much bigger than
x.
So the commonly discussed "long-tail" distribution is the power law distribution,
with tail distribution
for α > 1.
So does the long-tailed condition hold? Well,
which indeed has a limit of 1 as
x → ∞. So, indeed, the power law distribution is long-tailed.
Now, there is the question of whether Kyle was right/more exact than me. If all we're talking about is power-law distributions, then I suppose he is. Let me just emphasize that we are both technically correct, but he is more exact. According to Wikipedia (All hail Wikipedia!) there are distributions which are heavy-tailed and not long-tailed. I suppose the question is whether people in pop science are referring to these, and I suppose the answer is probably no.
“Fury said to
a mouse, That
he met in the
house, Let
us both go
to law: I
will prose—
cute you.—
Come I’ll
take no
denial: We
must have
the trial;
For really
this morning
I’ve
nothing
to do.
Said the
mouse to
the cur,
’Such a
trial, dear
sir. With
no jury
or judge,
would
be wasting
our
breath.’
’I’ll be
judge,
I’ll be
jury,’
said
cunning
old
Fury:
’I’ll
try
the
whole
cause,
and
condemn
you to
death.’”
Alice in Wonderland, Lewis Carroll
![[Wikipedia]](http://en.wikipedia.org/wiki/File:Serpiente_alquimica.jpg){kind=link}
