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

5) The MLSq (Bienaymé 1852; HS, pp. 66 – 71). Bienaymé correctlyremarked that least variance for each estimator separately was not asimportant as the minimal simultaneous confidence interval for all theestimators (as joint efficiency!). He assumed that the distribution **of** theobservational errors was known, made use **of** its first moments and evenintroduced the first four cumulants and the multivariate Gram – Charlierseries (Bru 1991, p. 13; Hald 2002, pp. 8 – 9). He determined thatconfidence interval by applying the principle **of** maximum likelihood,introducing the characteristic function **of** the vector **of** the errors and makinguse **of** the inversion formula. True, he restricted his choice **of** the confidenceregion, but derived here the χ 2 distribution.6) A branching process (Bienaymé 1845; HS, pp. 117 – 120). Bienayméhad formulated the properties **of** criticality **of** a branching process whileexamining the problem **of** the extinction **of** noble families that becameattributed to Galton. D. G. Kendall (1975) reconstructed Bienaymé’s pro**of**and reprinted his note.7) When investigating the stability **of** statistical frequencies (see also item2 above), Bienaymé (1840a; HS, pp. 108 – 110) expressed ideas thatunderlie the notion **of** sufficient estimators.10.3. CournotHe intended his main contribution (1843) for a broader circle **of** readers.However, almost completely declining the use **of** formulas, he hardlyachieved his goal. Recall also (§ 8.1) that Cournot passed over in silence theLLN. I describe his work as a whole; when referring to his main book, Imention only the appropriate sections. Chuprov (1925a/1926, p. 227) calledCournot the real founder **of** the modern philosophy **of** statistics. This seemsto be exaggerated. He did not substantiate and canonically prove the LLN(Chuprov 1905/1960, p. 60; 1909/1959, pp. 166 – 168), did not evenformulate that law.1) The aim **of** the theory **of** probability. It was The creation **of** methods forassigning quantitative values to probabilities (p. 181). He thus moved awayfrom Laplace (§ 7.1) who had seen the theory as a means for revealing thelaws **of** nature.2) The probability **of** an event. Cournot’s definition (§ 18) includedgeometric probability, which had been lacking any formula, and combined itwith the classical case. He (§ 113) also introduced probabilities unyieldingto measurement and (§§ 233 and 240.8) called them philosophical. Theymight be related to expert estimates whose treatment is now included in theprovince **of** mathematical statistics.3) The term médiane. This is due to Cournot (§ 34).4) The notion **of** randomness. Cournot (§ 40) repeated its ancientconnection with the intersection **of** chains **of** events (my § 1.1), and, in § 43,indirectly connected randomness with unstable equilibrium by remarkingthat a right circular cone, when stood on its vertex, fell in a randomdirection. Cournot (1851, § 33, Note 38; 1861, § 61, pp. 65 – 66) alsorecalled Lambert’s attempt to study randomness (see my § 6.1.3), and(1875/1979, pp. 177 – 179) applied Bienaymé’s test (§ 10.2-4) forinvestigating whether the digits **of** the number π were random butreasonably abstained from a final conclusion.91