Power Law May Not be the Best Model for Predicting Web Page Popularity
https://stats.stackexchange.com/questions/43893/do-unique-visitors-to-a-website-follow-a-power-law
It turns out that the power law as described in lecture may not be the best model predicting web page popularity. In the discussion referenced above, the answerer mentions a study that sample web pages and sorted them by unique user visits. The paper concluded that they have found a better predictor model using a model called the scale-sensitive Zipf-Mandelbrot distribution, even though public wisdom suggests that such distributions follow the power law.
The answerer of the discussion demonstrates the (possible) inaccuracy of the power law model by plotting the data on a log-vs-log scale instead of the regular linear scale. The purpose is to test the truth of the power law model. Since the equation of the power law is in the form y = c/(k^n), if the power law indeed holds, then the resulting data will form a straight line, as demonstrated below:
y = c/(k^n) -> log y = log c – n.log k,
which is a straight line since c and n are constants.
The answerer attributes this inaccuracy due to past studies merely relying on “eyeballing” the data after it has been converted on a log-vs-log scale. Now that more formal tests have been developed, we can eliminate this unreasonable reliance on the human eye to get more accurate and objective results.