On Tables of Random Numbers

Abstract

The editors of Semiotika i Informatika have felt it appropriate to publish a Russian translation of my article, which reflects a certain stage of my attempts to give meaning to the frequency interpretation of probability due to R. von Mises. The article was written during my stay in India in 1962 and published by the Indian journal Sankhyā,a very authoritative periodical in mathematical statistics in English-speaking countries, but little known here in the USSR. The reader familiar with the work of von Mises will perhaps notice the wider definition of the algorithm A used for selecting samples. But the main difference from von Mises is the strictly finite character of the whole approach and the introduction of a quantitative estimate of the stab ility of frequencies. The problem of bringing together estimates (4.3) and (4.4), despite its elementary character, apparently still awaits its solution. Further stages of my search in this direction are reflected in two notes, published in 1965 and 1969 in the journal Problemy Peredachy Informatsii. In Semiotika i Informatika, see V.V.Vyugin’s survey (1981, vyp. 16).

Sankhyā. Indian J. Statist. Ser.A. 1963, vol.25, N 4, 369–376

This article was published in Russian in the periodic collection Semiotika i Informatika (Moscow, VINITI,1982, vyp. 18, 3–13) and was prefaced by the short text especially written by A.N.Kolmogorov which appears here under the title “From the Author”. The text of the article itself is not the original (published in Sankhyā), but a new translation of the Russian text that appeared in Semiotika (Translator’s Note).