1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

5) Dependence between the decisions of judges and/or jurors. Cournot(1838; 1843, §§ 193 – 196 and 206 – 225) gave thought to this issue but hisstudy was hardly successful in the practical sense.6) A critical attitude towards statistics; a description of its aims andapplications (Chapters 7 and 8 and §§ 103 – 120). Statistics (§ 105) shouldhave its theory, rules, and principles, it ought to be most widely applied; itsmain goal was to ascertain the knowledge of the essence of things, to studythe causes of phenomena (§ 120) and the principe de Bernoulli was its onlypertinent sound foundation (§ 115). Statistics had blossomed exuberantlyand [the society] should be on guard against its premature and wrongapplications which might discredit it for some time (§ 103).7) Explanation of known notions and issues (§§ 64 – 65, 73 – 74).10.4. BuniakovskyHis treatise (1846) was the first comprehensive Russian contribution sothat Struve (1918) called him a Russian student of the French mathematicalschool. A list of his contributions is in Materialy (1917).1) The theory of probability. Buniakovsky (1846, p. I) correctlyattributed it to applied mathematics.2) Moral expectation (see § 6.1.1). Buniakovsky (1846, pp. 103 –122) independently proved Daniel Bernoulli’s conclusion that an equaldistribution of the cargo on two ships increased the moral expectationof the freightowner’s capital as compared with transportation on asingle ship. Later he (1880) considered the case of unequalprobabilities of the loss of the ships.3) Geometric probabilities (§ 6.1.6). Buniakovsky (1846, pp. 137 –143) generalized the Buffon problem by considering the fall of theneedle on a system of congruent equilateral triangles. His geometricreasoning was, however, complicated and his final answer, as Markov(Treatise, 1900/1924, p. 270) maintained, was wrong. EarlierBuniakovsky (1836 – 1837) remarked that the solution of suchproblems might help to determine the values of special transcendentalfunctions.4) Statistical control of quality. Buniakovsky (1846, Adendum)proposed to estimate military losses by sample data but his study washardly useful. He (1846, pp. 468 – 469) also indicated that his findingsmight facilitate the acceptance of a very large number of articles andsupplies only a fraction of which was actually examined.5) The history of the theory of probability. Buniakovsky was one ofthe first after Laplace to consider this subject and made a few offactual mistakes.6) Population statistics. Buniakovsky (1846, pp. 173 – 213)described various methods of compiling mortality tables, studied thestatistical effect of a weakening or disappearance of some cause ofdeath (cf. § 6.2.3), calculated the mean and the probable durations ofmarriages and associations and, following Laplace, solved severalother problems.After 1846, Buniakovsky continued these investigations. Hecompiled mortality tables for Russia’s Orthodox believers and tablesof their distribution by age (1866a; 1866b; 1874) and estimated thenumber of Russian conscripts ten years in advance (1875b). No one92

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