On the Frequency Distribution of Large Errors

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Abstract
In various papers published recently in the Journal and elsewhere, examples have been given in which the theoretical normal or gaussian distribution of errors does not correspond closely with the distributions found in practice; in particular the frequency of large errors is commonly underestimated by the normal law of errors. This discrepancy is discussed by Anderson who suggests that an exponential distribution may give a more realistic estimate of the frequency of large errors. A closely associated problem is that of determining the frequency distribution of the largest values occurring in a number of samples taken from some parent population. This problem has been solved theoretically for an important class of distributions and it is the object of this article to draw attention to this work and to show how it can be simply applied to practical problems, albeit in a rough and ready manner, without going far into the statistical details with which the subject abounds.

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