1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

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Concerning the rigor of the frequentist theory, witness Uspensky etal (1990, § 1.3.4):Until now, it proved impossible to embody Mises’ intention in adefinition of randomness that was satisfactory from any point of view.I ought to add, however, that Kolmogorov (1963, p. 369) hadessentially softened his viewpoint about that theory:I have come to realize that the concept of random distribution of aproperty in a large finite population can have a strict formalmathematical exposition.In the 19 th and 20 th centuries statisticians had been reluctant tojustify their studies by the Bernoulli LLN. They did not refer either tothe inverse law or to Poisson (which would not have changed much).Maciejewski (1911, p. 96) even introduced la loi des grands nombresdes statisticiens that only stated that the fluctuation of statisticalnumbers diminished with the increase in the number of trials.Romanovsky (1924, pt 1, p. 15) stressed the natural scientific essenceof the LLN and called it physical. Chuprov (1924, p. 465) declaredthat the LLN included either mathematical formulas or empiricalrelations and in his letters of that time he effectively denied that theLLN provided a bridge between probability and statistics.BibliographyBayes T. (1764), An essay towards solving a problem in the doctrine of chances.Phil. Trans. Roy. Soc., vol 53 for 1763, pp. 360 – 418. Reprint: Biometrika, vol. 45,1958, pp. 293 – 345.--- (1765), Demonstration of the second rule in the essay [of 1764]. Ibidem, vol.54 for 1764, pp. 296 – 325.Chuprov A. A. (1924), Ziele und Wege der stochastischen Grundlagen derstatistische Theorie. Nord. Stat. Tidskr., t. 3, pp. 433 – 493.Kolmogorov A. N. (1963), On tables of random numbers. Sankhya, Indian J.Stat., vol. A25, pp. 369 – 376.Maciejewski C. (1911), Nouveaux fondements de la théorie de la statistique.Paris.Romanovsky V. I. (1924 Russian), Theory of probability and statistics accordingto some newest Western scholars. Vestnik Statistiki, No. 4 – 6, pp. 1 – 38; No. 7 – 9,pp. 5 – 34.Uspensky V. A., Semenov A. L., Shen A. Kh. (1990 Russian), Can an(individual) sequence of zeros and ones be random? Uspekhi Matematich. Nauk, vol.45, pp. 105 – 162. This periodical is being translated cover to cover.140
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Studies in the History of Statistic
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Introduction by CompilerI am presen
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(Lect. Notes Math., No. 1021, 1983,
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sufficiently securely that a carefu
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is energy?) from chapter 4 of Feynm
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demand to apply transfinite numbers
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for stating that Ω consists of ele
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chances to draw a more suitable apa
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Let the space of elementary events
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2.3. Independence. When desiring to
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Eξ = ∑ aipi.Our form of definiti
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absolutely precisely if the pertine
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where x is any real number. If dens
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probability can be coupled with an
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Nowadays we are sure that no indepe
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λ = λ(T)with λ(T) being actually
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(1/B n )(m − A n )instead of the
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along with ξ. For example, if ξ i
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µ( − p0) ÷np0 (1 − p0)nhas an
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distribution of the maximal term |s
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ξ (ω) + ... + ξ (ω)n1n{ω :|
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P{max ξ(t) ≥ x} = 0.01, 0 ≤ t
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1. This example and considerations
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IIV. N. TutubalinTreatment of Obser
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structure of statistical methods, d
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Suppose that we have adopted the pa
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and the variances are inversely pro
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It is interesting therefore to see
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is applied with P(t) being a polyno
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ut some mathematical tricks describ
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It is clear therefore that no speci
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of various groups of machines, and
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nnA(λ) x sin λ t, B(λ) = x cosλ
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of the mathematical model of the Br
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dF(λ) = f (λ) dλ, so that B( t
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usually very little of them. Indeed
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This is the celebrated model of aut
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applications of the theory of stoch
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achieved by differentiating because
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u(x 1 , x 2 , t 1 , t 2 ) = v(x 1 ,
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Reasoning based on common sense and
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answering that question is extremel
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IIIV. N. TutubalinThe Boundaries of
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periodograms. It occurred that work
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Page 95 and 96: In the purely scientific sense this
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Page 101 and 102: values of (2.1) realized in the n e
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Page 111 and 112: 258 - 82 - 176 cases or 68.5% of al
Page 113 and 114: The Framingham investigation indeed
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Page 117 and 118: What objections can be made? First,
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Page 121 and 122: Kolman E. (1939 Russian), Perversio
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Page 125 and 126: which means that sooner or later th
Page 127 and 128: The foundations of the Mises approa
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Page 131 and 132: 4.3. General remarks on §§ 4.1 an
Page 133 and 134: BibliographyAlimov Yu. I. (1976, 19
Page 135 and 136: processes are now going on in the s
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Page 139: VIOscar SheyninOn the Bernoulli Law
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1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

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