On the Conformity-to-a-Law of the Distribution of Errors in a Series of Observations

Part of the Springer Series in Statistics book series (SSS)


In order to specify completely the assumptions underlying the discussion to follow, we will suppose that we are dealing with some process in which the value of a measurable characteristic B varies with another, A (as, for example, the pressure of a body of steam varies with temperature, or the like). Then, on the one hand, for a series of values a 1, a 2a n of the determining variable A, let the corresponding values b 1, b 2b n of B be obtained by direct measurement; on the other hand, suppose that some theoretical formula, expressing the dependence as B = F(A), gives calculated values β 1, β 2, β n corresponding to a 1,… a n .1 The question is now: what is the probability that the n differences
$$ \beta _1 - b_1 = x_1 ...\beta _n - b_n = x_n $$
arise entirely from random errors of observation?


Prob Ability Functional Determinant Observational Process Successive Error Probability Apriori 
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  1. 1.
    Situations occurring in practice can in most cases be reduced to this simple scheme, even when more than two variables are involved.Google Scholar
  2. 1.
    There is evidently no loss of generality in immediately taking zero as one of the limits.Google Scholar
  3. 1.
    The use of an integral similar to the above as discontinuity factor is familiar to me through the lectures of Professor Riemann in Göttingen.Google Scholar
  4. 1.
    s. Baltzer. Theorie der Determ. ( Theory of Determinants presented with reference to the original sources) (1857). Leipzig: S. Hirzel.Google Scholar
  5. 1.
    ; A proof of this theorem can be found in Zeitschr. f. Math. u. Phys. Vol. VII, 1862, p. 440. [G. Zehfuss: Applications of a special determinant, idem, pp. 439— 445.]Google Scholar
  6. 1.
    M.A. Stern, Lehrb. d. algebr. Analysis [Leipzig, C.F. Winter, 1860] p. 385.Google Scholar

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© Springer Science+Business Media New York 2001

Authors and Affiliations

  • E. Abbe

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