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Most people don't understand log-log graphs. Also, taking the log-log is so powerful that even distributions that don't strictly follow a power law can look as
by loeber 10y ago
Most people don't understand log-log graphs. Also, taking the log-log is so powerful that even distributions that don't strictly follow a power law can look as if they're approximately following a straight line.
- noobermin 10y agoPlot two graphs, one loglog, one not. Also, "nearly linear" on a log-log graph does mean almost power law.
- smallnamespace 10y agobeing roughly straight on a log-log plot is a necessary but not sufficient condition for power-law behavior Source: https://arxiv.org/abs/0706.1062 https://arxiv.org/abs/0706.1062, p.15 pp. 24-29 have nice log-log plots of various data sets, along with whether they can plausibly described as power law distributions. 'Wealth', interestingly enough, looks like a pretty straight line, but fails the statistical test badly. Btw, if you just take logs and run a regression to estimate the exponent, you get a highly biased estimate. In general, it's much better to do a direct statistical test, although the method described in the paper is somewhat involved.
- noobermin 10y agoI like what you shared. I actually can't believe I haven't seen that paper before (it has >4k citations ffs), but I admit, I work in a less statistical side of physics. What I'll say is that what something is is a fuzzy term, although I generally agree what you mean especially about a power law says about the behavior in the tails especially. That comes from thinking a small deviation on the tail is "small" due to optics and not realizing it is deviation on orders of magnitude. That might be what the replier to my comment was referring to. That's why "two graphs" is usually a good answer. PS Also, I would never fit a straight line on a loglog or semilog graph, nor should anyone ever. People who do that don't understand what least squares is at all.
- kevin_thibedeau 10y agoIt can still be useful to do a polynomial regression on log-log data that doesn't quite obey a power law.
- noobermin 10y agoNo I meant log'ing the bins and then doing linear regression and calling that an "exponential fit". Not so. A polynomial is a power law...with more terms.
- marcosdumay 10y agoSorry, but I'll state the exact opposite here. It is much easier to check if the points fall in a straight line than a perfectly draw exponential. Are you sure that graph is a power law? Are you sure it isn't a thick-tailed hyperbole or some hyperexponential?
- Rangi42 10y ago"Everything is linear if plotted log-log with a fat magic marker." — Mar's Law