Abstract
THREE brief but important notes on the theory of the law of error were communicated to the Royal Academy of Sciences at Stockholm last year by Mr. Charlier, director of the astronomical observatory at Lund. The first of these (“Ueber das Fehlergesetz”) is a discussion on the lines, generally, laid down by Laplace. An “error“ is supposed to be given by the sum of a large number of elementary errors, each with its own law of frequency; these laws need not be the same, but are subject to the condition that the frequency should not fall off with great rapidity on either side of the mode. On this condition, the law reached is the known expansion in terms of the normal function and its differentials, recently discussed in detail by Prof. Edgeworth (Camb. Phil. Trans., vol. xx.). In his second note (“Die zweite Form des Fehlergesetzes”) Mr. Charlier discusses the complementary case, in which the condition stated does not hold, supposing, for instance, that each elementary error can only take the value zero or a, and that the probability of a is very small. The normal function of the former series is now replaced by an auxiliary function of more complex form. These two laws are referred to as Type A and Type B. The third note (“Ueber die Darstellung willkbrlicher Funktionen”) bears on the general mathematical method employed.
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Y., G. The Theory of Frequency-Distributions 1 . Nature 74, 187 (1906). https://doi.org/10.1038/074187a0
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DOI: https://doi.org/10.1038/074187a0