By Dauxois J.-Y., Druihlet P., Pommeret D.

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X/dx signified the probability of an error lying between x and x C dx. The phrase “distribution function” is—even today—managed differently by different authors. X < x/ (Kolmogorov). ” 20 Farebrother [1999] provides a history of the theory of errors that gives special consideration to the problems of linear algebra in the original notation. 21 One exception is the inversion formula for characteristic functions; see Sect. 4. Furthermore, in some estimates it is necessary to consider whether a “<” or a “Ä” is correct.

19) where the approximation becomes all the better the larger s is, and the difference between the left and the right side becomes “infinitely small” with “infinite” s. 19) only for the special case D < 0. Poisson was convinced that this CLT was also valid for discrete random variables. 19 As with Laplace, the CLT for Poisson was an important tool of classical probability, but not an autonomous mathematical theorem. 18) for characteristic functions, and he discussed counterexamples to an overall validity of asymptotic normal distributions for sums.

H jB/ for certain “hypothetic” causes H which may have entailed the observed results B. Hj / are unknown in most cases, one is often forced to the “subjective” assumption of the Hj being equiprobable. 3 In this context, the problem of calculating the probability distribution of the sum of angles of inclination, which were assumed to be determined randomly, as well as the related problem of calculating the probabilities of the deviations between the arithmetic mean of data which were afflicted by observational errors and the underlying “true value,” became especially important.