THE FOUNDATION FOR THE APPLICATION OF PROBABILITY THEORY TO STATISTICS

TCHEBYCHEFF, P. [CHEBYSHEV] [TCHEBYCHEV].

Sur deux théorèmes relatifs aux probabilités.

Berlin, Stockholm, Paris, Almqvist & Wiksell, 1890. 4to. As extracted from "Acta Mathematica", Vol, 14, 1890. No backstrip. A fine and clean copy. Pp. 305-15.

First translation of Chebyshev's landmark paper (first published in Journal of the The St. Petersburg Academy in 1887) in which he laid the foundation for the application of probability theory to statistics, generalizing the theorems of Moivre and Laplace. It also generalized the theory of integral beta function. This led him to find an algorithm for finding an optimal solution in a system of linear equations with an approximate solution is known.

"In the 1860's Chebyshev returned to the theory of probability. One of the reasons for this new interest was, perhaps, his course of lectures on the subject started in 1860. He devoted only two articles to the theory of probability, but they are of great value and designate the beginning of a new period in the development of this field. In the article of 1866 Chebyshev suggested a very wide generalization of the law of large numbers. In 1887 he published (without extensive démonstration) a corresponding generalization of the central limit theorem of Moivre and Laplace." (DSB).

"Chebyshev and many of his students were often cold and skepticall towrads various important achievements in Western European mathematics. In the two-hundred-year development period in probability theory its main achievements were the limiting theorems: the law of large number and the de Moivre-Laplace theorem. But the confines of applicability of these theorems and their further refinements and generalizations were not satisfactory. The second basic problem that occupied Chebyshev's attention was the central limit theorem. However, only in 1887 in the Proceedings of the Academy of Sciences was Chebyshev's paper devoted to this subject published." (Maistrov, Probability and Mathematical Statistics, P. 202).

Order-nr.: 49619