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Chris Anderson

Sigh. I was with you right up until you introduced the facebook data. A Long Tail is a powerlaw distribution, which looks exactly like what you've shown. All powerlaws have a huge drop-off like that--but the tail being long (get it?) the area under what appears to almost nothing adds up to a lot. The only way you can tell whether it really does conform to the theory or not is to plot it log-log and see if it's a straight line.

Anand Rajaraman

Chris, not all power laws lead to heavy tails. Depending on the exponent of the power law, you can get either the classic hits-dominated model, or a heavy tail. The Facebook data does show that we have a hits-dominated marketplace.

That said, I think you were on to something in that the internet transforms media. It's just not in the narrow way you describe in your book. Time for a new edition?

Jason Rennie

My understanding has been that all power laws are heavy-tailed. That understanding seems to jive with Wikipedia definitions: a power law has pdf p(x) ~ ax^k; a dist is heavy-tailed if \lim_{x \to \infty} e^{\lambda x} p(x) = \infty for all \lambda > 0. I don't see how a power law can outweigh an exponential in the limit as x approaches infinity. Am I missing something?

http://en.wikipedia.org/wiki/Power_law

http://en.wikipedia.org/wiki/Heavy-tailed_distribution

D. Liu

@Jason
Yes, as far as a function is sub-exponential, it results a 'heavy tail'. That's the mathematical definition.

Anand Rajaraman

Jason, D. Liu: Yes, you guys are right as far as the mathematical definition is concerned. But the actual heaviness of the tail, in terms of practical consequences, depends on the exponent. Details at this page:

http://anand.typepad.com/datawocky/not-all-powerlaws-have-lo.html

Johan

Anand, this is exactly the thing I wanted to say in the comment feed on Anitas article.

http://conversationstarter.hbsp.com/2008/07/the_long_tail_debate_a_respons.html#c026062

Has there been any analysis made on the rate of change of the hits in any specific industry? My gut feeling (based on Lily Allen, Kate Nash, every deep house produced you can think of and etc etc) is that in the music industry the rate of change is significantly higher now than before.

Shahar

Chris is of course correct, and that is part of the reason for my frustration with lots of long tail discussions. There's a simple and straightforward way to see whether data fits a long tail description or not, and yet people choose to ignore it most of the time, turning to arbitrary hand-waving arguments with a few numbers and percentages thrown in.
I am especially annoyed by this being the case in Elberse's paper, but I managed to find sufficient data for partial analysis in one part of her paper. I was hoping to find that her data fits a long-tailed distribution but found out that an exponential one is a much better fit.
This makes me even more puzzled.
Anyway, you can find it here:
http://longtailanalysis.blogspot.com/2008/07/shes-got-point-or-three.html

Shahar

Chris is of course correct, and that is part of the reason for my frustration with lots of long tail discussions. There's a simple and straightforward way to see whether data fits a long tail description or not, and yet people choose to ignore it most of the time, turning to arbitrary hand-waving arguments with a few numbers and percentages thrown in.
I am especially annoyed by this being the case in Elberse's paper, but I managed to find sufficient data for partial analysis in one part of her paper. I was hoping to find that her data fits a long-tailed distribution but found out that an exponential one is a much better fit.
This makes me even more puzzled.
Anyway, you can find it here:
http://longtailanalysis.blogspot.com/2008/07/shes-got-point-or-three.html

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