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A Version of Hagen's Proof of the “Law of Error.”
Published online by Cambridge University Press: 20 January 2009
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Hagen's proof (1837), as described in the 8th edition of Mansfield Merriman's “Method of Least Squares,” is based on the assumption that the error may be supposed to consist of the algebraic sum of an infinite number of infinitesimal errors of equal amount ε, each one of which is equally likely to be positive or negative. Thus if 2m is the number of the infinitesimal errors, the probability of the error x ≡ 2p ε occurring is
and the maximum value of P occurs when p = 0, and is
.
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- Copyright © Edinburgh Mathematical Society 1919
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* This is equivalent to the assumption that the probability that the error lies between two finite values differing by a finite amount, is finite.
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