36. Studies in History of Statistics. Berlin, 2009
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Studies in the History of Statistics and Probability Collected Translations Compiled and translated by Oscar Sheynin Berlin, 2009 1 ISBN 3-938417-94-3 Oscar Sheynin, 2009 2 Contents Introduction by Compiler I. M. V. Ptukha, Sampling investigations of agriculture in Russia in the 17 th and 18 th centuries, 1961 II. A. A. Chuprov, The problems of the theory of statistics, 1905 III. N. K. Druzinin, Scientific contents of statistics in the literature of the 20 th century, 1978 IV. E. E. Slutsky, Theory of Correlation and Elements of the Doctrine of the Curves of Distribution, Introduction, 1912 V. E. E. Slutsky, Statistics and mathematics. Review of Kaufman (1916), 1915 – 1916 VI. Oscar Sheynin, Karl Pearson 150 years after his birth, 2007 VII. H. Kellerer, W. Mahr, Gerda Schneider, H. Strecker, Oskar Anderson, 1887 – 1960, 1963 VIII. S. Sagoroff, Oskar Anderson, Obituary, 1960 IX. V. I. Riabikin, Oskar Anderson, Chuprov’s student, 1976 X. O. Anderson, To the memory of Professor A. A. Chuprov Junior, 1926 XI. Oskar Anderson, Ladislaus von Bortkiewicz, 1932 XII. Oskar Anderson, On the notion of mathematical statistics, 1935 XIII. Oskar Anderson, Mathematical statistics, 1959 XIV. P. P. Permjakov, From the history of the combinatorial analysis, 1980 XV. K.-R. Bierman, Problems of the Genoese lotto in the works of classics of the theory of probability, 1957 XVIa. V. Ya. Buniakovsky, Principles of the Mathematical Theory of Probability, Extracts, 1846 XVIb. A. Ya. Boiarsky, E. M. Andreev, The Buniakovsky method of constructing mortality tables, 1985 XVII. A. M. Liapunov, Pafnuty Lvovich Chebyshev, 1895 XVIII. A. A. Konüs, On the definition of mathematical probability, 1978 XIX. Oscar Sheynin, Review of Ekeland (2006), unpublished XX. Oscar Sheynin, Antistigler, unpublished 3 Introduction by Compiler Following is a collection of papers belonging to statistics or probability theory and translated from Russian and German; in some cases, the dividing line is fuzzy, as it ought to be expected. They are designated by Roman numerals which I am also using just below when providing some general remarks concerning them. Authors of some rather long papers had subdivided them into sections; otherwise, I myself have done it (and indicated that the responsibility is my own by numbering them [1], [2], etc). References in this Introduction are to the Bibliographies appended to the appropriate papers. Finally, in cases of cross references in the main text, these are such as [V, § 2] and the unsigned Notes are my own. I. Mikhail Vasilievich Ptukha (1884 – 1961) was a statistician and demographer much interested in the history of statistics, He was a Corresponding Member of the Soviet Academy of Sciences. Ptukha describes the elements of sampling in agriculture during the period under his study. This could have been dealt with in a much, much shorter contribution, but he also tells us which types of estates had applied these elements and how exactly was each procedure done to ensure more or less reliable data. Of course, much more interesting is the practice of sampling for checking the coining in England which is seen in the very title of Stigler (1977): Eight centuries of sampling inspection. The trial of the Pyx . Sampling in agriculture, however, should also be documented. Ptukha begins by saying a few words about sampling at the turn of the 19 th century. On Kiaer (whom Ptukha mentions) and other statisticians of that period, both opposing and approving sampling, see You Poh Seng (1951). It is also opportune to add that Seneta (1985) and Zarkovich (1956; 1962) studied sampling in Russia during the early years of the 20 th century. Meaning of special terms and old Russian measures Dvortsovaia : dvorets means palace , and dvortsovaia is the appropriate adjective apparently concerning the Czar’s palace. Sloboda : suburb Stolnik : high ranking official at court Tselovalnik : the man who kissed ( tseloval ) the cross when taking the oath of office. In particular, he took part in the judicial and police surveillance of the population Voevoda: governor of province Volost : small rural district Votchina : patrimonial estate owned by the votchinnik Chetverik : 18.2 kg Dessiatina : 1.09 hectare Pood : 16.4 kg Sazhen : 2.13 m Sotnitsa : some unit; sotnia means a hundred II. In 1909, Chuprov published his Russian Essays on the Theory of Statistics which became extremely popular and at the time, and even now Russian statisticians consider it a masterpiece although Druzinin [III] critically surveyed his work; my remarks below ought to be supplemented 4 by his paper. Among mathematicians, Markov (1911/1981), provided a critical comment. Thus (p. 151), the Essays “lack clarity and definiteness”. Chuprov preceded his Essays by two long German papers (1905; 1906) the first of which I am translating below from its Russian translation made by his closest student N. S. Chetverikov but I have also checked many places of the Russian version against the original and provide the page numbers (in bold type) of the original to show that the translation was correct. In one case, however, Chetverikov made a mistake and I have additionally inserted there my own translation. I left out many passages which either seemed not really needed or much more properly belonged to philosophy. Indeed, Chuprov’s exposition was (and to a certain extent remains in the translation) verbose which was possibly occasioned by the author’s wish to satisfy his readers (and perhaps corresponded to his pedagogical activities at Petersburg Polytechnical Institute) and Markov’s remark is appropriate here also. In 1910 – 1917 Chuprov corresponded with Markov (Ondar 1977) after which (and partly during those years) his most important contributions had been made in the mathematical direction of statistics; I do not say mathematical statistics since that discipline had only begun to emerge in those years. Seneta (1982; 1987) described some of Chuprov’s relevant discoveries, but my translation gave me an opportunity to provide some additional related information. 1. Resolutely following Lexis and Bortkiewicz, Chuprov paid much and even most attention to the justification of statistics by the theory of probability. The problem facing statisticians in those times (also much earlier and apparently somewhat later) consisted in that they, perhaps understandably, had been interpreting the Bernoulli theorem in a restricted form, and even Lexis (below) had wavered on this issue. They contended that that theorem was only useful when the theoretical probability (and therefore the equally probable cases) really existed. Actually, we may imagine its existence (if only not contradicting common sense) given its statistical counterpart. At least towards the end of the 19 th century the appearance of the non-Euclidean geometry had greatly influenced mathematicians who became quite justified to treat imaginary objects. Chuprov, although a mathematician by education, had never taken a resolute stand; here, his relevant statement in § 3.2 was at least not definite enough. Lexis wavered over this issue. At first, he (1877, p. 17) stated that equally probable cases might be presumed when a statistical probability tended to its theoretical counterpart, but there also he (p. 14) remarked that, because of those cases the theory of probability was a subjectively based discipline and he (1886, p. 437) later repeated that idea. And in 1903 he (p. 241 – 242) confirmed his earliest pronouncement that the existence of such cases was necessary for “the pattern of the theory of probability”. Another point pertaining to mathematical statistics if not theory of probability is Chuprov’s failure to state that the ratios of the different measures of precision to each other depended on the appropriate density function. True, he only followed the general (including Lexis’) attitude of the time, but a mathematician should have been more careful. 2. Instead of enthusiastically supporting the Lexian theory of stability of statistical series in 1905 (see below), he became its severe critic and 5 finally all but entirely refuted it, which his students soon found out; it is strange that his work in that direction is still barely known outside Russia. Chetverikov inserted a special footnote referring to his (although not the first) relevant paper. Already in 1914, even before publishing his decisive German papers on the stability of series, Chuprov thought about abandoning the Lexian theory. In a letter No 135 to him of that year Bortkiewicz (Bortkevich & Chuprov 2005) disagreed about “shelving” the Lexian coefficient Q. 3. Bortkiewicz’ law of small numbers (1898), which he considered (and which indeed was) inseparably linked with the Lexian theory, was another issue about which Chuprov at least partly changed his opinion. Moreover, since the two scientists had been extremely close to each other with Bortkiewicz stubbornly clinging to his law, it is even possible that Chuprov just did not publicly express his opinion. In 1905, Chuprov approved Bortkiewicz’ innovation but later he (1909/1959, p. 284n) listed four possible interpretations of that law; there also, on p. 277, he remarked, although without naming Bortkiewicz, that The coefficient Q cannot be a precise measure of the deviations of stability from its normal level: it does not sufficiently eliminate the influence of the number of observations on the fluctuations . Then, in 1916 (Sheynin 1990/1996, p. 68), he informed Markov that It is difficult to say to what extent does it enjoy recognition of statisticians since it is not known what, strictly speaking, should be called the law of small numbers. Bortkiewicz did not answer my questions formulated in the Essays [see above] either in publications or in writing. I did not question him to his face at all since he regards criticisms of that law very painfully . The title of my paper (2008) explains my understanding of the law of small numbers. See also Heyde & Seneta (1977, § 3.4).