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June 16, 2010


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Cellphone data usage is almost certainly a fat-tailed distribution, not a normal one. The second graph says absolutely nothing about the first, and shame on this article for promoting the idea that every distribution is normal.

I hate the cellphone companies too, but this is silly,
Bill Mill

It would be great to see the data because this must not be normal and must be fat tailed (as Bill stated) because with that SD then the 99% is less than 700, not the 800 in the chart.

Not to mention that the probability of using less than 0 MB of data is 0. With an "average" of 200 MB and a standard deviation of 159 MB, a normal distribution is going to be significantly wrong. My guess is a gamma distribution, but others could make sense.

Also, I'd take the "average" of 200 MB as the mode, not the mean, given the graph.

You can't model these data by a normal distribution. Note that your model implies that a large number of cellphone users use NEGATIVE megabytes. The real usage is bounded below by zero, but is unbounded above. Simple models for this situation include lognormal and gamma.

Use "Empirical Cumulative Distribution Function", ecdf() or something instead.

I use about 18G of mobile data monthly with 7 Mbit/s modem. New modems are 21 Mbit/s. Theoretically my plan is capped to 3G/month but the operator doesn't seem to care. This costs 13 euros in a month.


Its highly likely (ie its a regular mistake) that the top distribution is a fit to data with some super user peaks that are not apparent (should have loessed it).

So the 97 percentile is (probably) in the right place but the curve itself a poor representation.

Agree with the above comments: This is not a normal distribution. The leftmost bound of x axis should be 0 (not negative) and using standard deviation of normal distribution is not correct. Need to use another distribution...

-Ralph Winters

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