One of the more striking results (at least to me) in Nate
Silver’s “The Signal and the Noise” is the ubiquitous nature of power laws.
They appear to accurately describe such randomly occurring events as
earthquakes (chapter 5) to terrorist attacks (chapter 13).

A good introduction to power can be found here. I will say that
a power law can describe data if, after computing an empirical cumulative
distribution function, you log both axis (to create a “log – log” plot) and if
the relationship appears to be linear then it is a power law.

Can a power law describe such apparently random events as
indiscriminate mass shootings such as the Newtown, CT Massacre? Mother Jones (here) has a dataset that includes 62 Mass Shootings from August 1982 up to December
2012 and the number of total victims (these include injured).

Below are the two graphs I made to distinguish. The first
one is just a normal ECDF, the second graph is a log – log of the first.

It appears the log – log fits the data much more accurately
than the first. It therefore appears that number of victims in mass shootings follows a power law.

So I know these aren't REALLY CDF's. But the Step - Function idea is similar enough that I use the term

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