Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 202)


A short description of the content of statistics is not easy to give. An examination of the historical development of the notion statistics1 indicates that for a long time it was taken to mean the description of “national peculiarities” (such as population size, land conditions and economic data collection). Only in recent times have statistical concepts penetrated into the natural sciences (Boltzmann, Gibbs, Maxwell). Resting on the fundament of probability theory, which has rapidly developed since the turn of the century, mathematical statistics has also grown exceedingly rapidly in the last forty years and its methods have been enriched by a store of ideas that threatens to defy cataloging. Statistical considerations appear today in the most varied fields of astronomy, biology, medicine, psychology, physics and sociology.


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  1. 1.
    See W. Winkler, Grundriß der Statistik I, 2nd ed.: Manzsche Verlagsbuchhandlung, Vienna 1947, 1 ff. which also contains a number of historical remarks on statistics.Google Scholar
  2. 2.
    loc.cit.1, 96–97.Google Scholar
  3. 3.
    From „Permanenzen der Österreichischen Casino AG.“ December 1952.Google Scholar
  4. 4.
    R. V. Mises, Math. Z. 4, 1–97 (1919) or Wahrscheinlichkeitsrechnung und ihre Anwendungen in der Statistik und theoretischen Physik. (Vorlesungen aus dem Gebiet der angewandten Mathematik, Vol. I), Deuticke, Leipzig-Wien 1931.MathSciNetCrossRefGoogle Scholar
  5. 5.
    For investigations in this direction see P. Cantelli, W. Feller, M. Frechet, R. v. Mises, J. F. Steffensen and A. Wald, Les Fondements du Calcul des Probability (Actualites scientifiques et industrielles 735). Hermann & Cie, Paris 1938. Recently these investigations have been reconsidered and essentially enriched by adding new ideas. Cf. CP. Schnorr: Zufalligkeit und Wahrscheinlichkeit. Eine algorithmische Begründung der Wahrscheinlichkeitstheorie (Lecture Notes in Mathematics) Springer-Verlag, Berlin-Heidelberg-New York 1971.Google Scholar
  6. 6.
    A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung (Ergebnisse der Mathematik und ihrer Grenzgebiete), Springer-Verlag, Berlin 1933.Google Scholar
  7. 7.
    See A. Renyi, Wahrscheinlichkeitsrechnung. Mit einem Anhang über Informationstheorie (Hochschulbücher für Mathematik, Vol. 54), VEB Deutscher Verlag der Wissenschaften, Berlin 1962. 1 ff.Google Scholar

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© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  1. 1.University of ViennaAustria

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