One can compare the estimated probability distribution for the global land anomaly with that of the normal and Cauchy distributions. It is an intermediate of the two distributions with a r.m.s. deviation of 0.0867 for the best fitting Cauchy distribution and 0.0904 for a normal distribution with the same standard deviation.
The observed deviations of the anomalies from the annual average has a sharper peak and more distant outliers than a normal distribution but it is not as extreme as the Cauchy distribution having a well defined mean and standard deviation. An example of a process for which the Cauchy distribution applies is that of the Lorentzian function for the distribution of radiation in a spectral line of an atom.
Supplemental (Nov 13): Lorentz discusses the absorption distribution in The Theory of Electrons (1916) in §133-136 and Notes 60-62.
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