Tuesday, November 12, 2013

Comparison of the Anomaly Distribution with Other Probability Distributions

  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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