kniga 7 - Probability and Statistics 1 - Sheynin, Oscar

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4. He thoroughly remarks:A large number of accidents in breweries (14% in 1887 according to German data) isoccasioned by carting, 18%, by loading, unloading and carrying barrels. The coefficient ofrisk will consequently be quite different for breweries selling beer on the spot and thosehaving a vast region of customers; for those carting beer and breweries sending it byrailway.5. {Table 3 provides separate data on industrial (1887) and agricultural (1891) enterprisesin connection with 16 different structures, procedures etc. For example, Item 3, machinery inthe proper sense except for lifting gear in industrial enterprises: 17.55% of all the accidents,3.21% of all the accidents, 3.21 % of that per cent proving fatal; Item 13, water-bornetransportation, 0.99% and 74.05% respectively. Table 4 shows figures for the same two kindsof enterprises and years and lists 13 items connected with the second main cause. Thus, lackof safety structures in agricultural enterprises (Item 2), 10,64% and 11.35% respectively;thoughtlessness and intoxication (Item 6), 1.98% and 1.51% respectively.}6. However interesting are these data in themselves, they should be interpreted verycautiously. In logging, Jottrand indicates,459 accidents were caused by machines, 273 of them by circular saws and only 17 byband-saws. Are we therefore justified in recommending the latter as comparatively lessdangerous instead of the former? Not at all since it is likely that the difference between thenumbers was simply caused by the circular saw being much more in use than the band-saw.In general, it would be delusive to regard the numbers in the first column as indicators ofthe appropriate risks.ReferencesOn the legal aspect of occupational accidents:1. Handbuch der Unfallversicherung, 2 nd edition. Leipzig, 1896, pp. 28 – 78.2. Rosin, Das Recht der Arbeiterversicherung, Bd. 1, 1893, pp. 273 – 290.3. Piloty, R. Das Reichs-Unfallversicherungsrecht, Bd. 1, 1891, pp. 184 – 213.4. Menzel, Adolf, Die Arbeiterversicherung nach österreichischem Rechte. Leipzig, 1893,pp. 279 – 295.On the methods and results of the statistics of occupational accidents:1. Amtliche Nachrichten des Reichs-Versicherungsamt. Berlin, from 1885. Specialstatistics of industrial Genossenschaften for 1887 is in its Sechster Jahrgang (1890, p. 199ff).Similar statistics of agricultural Genossenschaften for 1891 is in its Neunter Jahrgang (1893,p. 231ff).2. Statistisches Jahrbuch für das Deutsche Reich, beginning with its 9 th Jahrgang (1888)contains brief information on the same subject.3. Die Gebärung und die Ergebnisse der Unfallstatistik der Arbeiterunfallversicherungs-Anstalten. Wien. Data for Austria.4. Congrès International des Accidents du Travail. Exposition universelle de 1889. Paris,1889 and 1890. Congrès …, 2 nd session, Bern, 1891. Congrès …, 3rd session, Milan.5. Bödiker, T. Die Arbeiterversicherung in den europäischen Staaten, 1895.6. Yarotskij, V.G. 0 0 (Insurance of Workers in onnection with the Responsibility of theOwners). Psb, 1895.
10. Anderson, O. Letters to Karl PearsonUnpublished; kept at University College London, Pearson Papers, NNo. 442 and 627/2Foreword by TranslatorOskar (Nikolaevich) Anderson (1887 – 1960) was Chuprov’s student and the lastrepresentative of the Continental direction of statistics. Little known information about him isin Sheynin (1996, §7.8). There also, in §15.6, the reader will see that on June 9, 1925,Anderson had sent Pearson a manuscript and that Pearson at once agreed to publish it inBiometrika. Note that the letters below were written later.I am grateful to University College London for allowing me to publish the followingletters which are kept by them (Pearson Papers NNo. 442 and 627/2). Both letters devoted tothe variate difference method are from Anderson who studied it from 1911 (when he wrotehis dissertation on the coefficient of correlation and its application to secular series) onwardand, together with Student (Gosset), was its co-creator. In particular, two from among hispapers that appeared in Biometrika (1923; 1926 – 1927) treated the same issue. In the secondof these, Anderson (p. 299/45) briefly outlined the history and the essence of that method.His letters below precede the second Biometrika paper; the second letter makes it clear thatPearson had tentatively agreed to grant Anderson 15 – 20 pages for publishing his not yetcompleted manuscript. Actually, however, the article of 1926 – 1927 occupied some 60pages which testifies that Pearson highly appreciated it. Then, Anderson desired to see hismanuscript translated from German to English, but that did not happen, perhaps owing to itsgreat length.I believe that the publication of the Anderson letters, in spite of the existing Biometrikaarticle, will not be amiss. His Ausgewählte Schriften, Bde 1 – 2, were published in Tübingenin 1963 and his latest biography written by Heinrich & Rosemarie Strecker is in Statisticiansof the Centuries (2001), Editors C.C. Heyde, E. Seneta. New York, pp. 377 – 381.* * *Letter No. 1Professeur Oskar Anderson, Varna, Ecole Supérieure de Commerce (Bulgarie)Varna, den 27. November 1925Sehr geehrter Herr Professor!In Ihrer Publikation (Pearson & Elderton 1923, p. 308) ist es zu lesen:We think it safe to say that there really does exist a substantial negative correlationbetween deaths of the same group in the first and second years of life. It is not as great as wefound it in the previous paper using hypotheses, which, we admit, ought to have been tested;but it is quite adequate to indicate that natural selection is really at work.Ich glaube beweisen zu können, daß Sie und Frl. E.M. Elderton hier der W.Person’schen{Persons’schen}Kritik gegenüber unnützerweise nachgegeben haben und daßIhre ursprünglichen Koeffizienten, welche Sie in der Arbeit Pearson & Elderton (1915)veröffentlicht haben, denjenigen der eingangs erwähnten Schrift jedenfalls in nichtsnachstehen und ihnen zum mindesten ganz ebenbürtig an die Seite gestellt werden können.Wie Sie sich erinnern werden, haben Sie in der letzteren zur ursprünglichen Methode IhresBiometr. Laboratoriums zurückgegriffen (1923, p. 284):
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of All Countries and to the Entire
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(Coll. Works), vol. 4. N.p., 1964,
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individuals of the third class, the
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From the theoretical point of view
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Second case: Each crossing can repr
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On the other hand, for four classes
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f i = i S + i , i = 1, 2, 3, 4, (
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f 1 = C 1 P(f 1 ; …; f n+1 ), C 1
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ut in this case f = 2 , f 1 = 2 ,
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I also note the essential differenc
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A 1 23n1 + 1 A 1 A 1 … A 11A 2 A
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coefficient of 2 in the right side
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h(A r h - c h A r 0 ) = - A r0we tr
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Notes1. Our formulas obviously pres
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Bernstein’s standpoint regarding
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Corollary 1.8. A true proposition c
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It is important to indicate that al
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ut for the simultaneous realization
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devoid of quadratic divisors and re
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propositions (B i and C j ) can be
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A ~ A 1 and B = B 1 , we will have
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included in a given totality as equ
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For unconnected totalities we would
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proposition given that a second one
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On the other hand, let x be a parti
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totality is perfect, but that the j
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In this case, all the finite or inf
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probabilities p 1 , p 2 , … respe
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where x is determined by the inequa
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totality of the second type (§3.1.
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x = /2 + /(23) + … + /(23… p n
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that the fall of a given die on any
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infinitely many digits only dependi
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10. (§2.1.5). Such two proposition
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F(x + h) - F(x) = Mh, therefore F(x
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“confidence” probability is bas
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x1+ Lp n (x) x1− Lx1+ Lf(t)dt < x
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|(x 1 ; t 0 ; t 1 ) - 1 t0tf(t)dt|
Page 81 and 82: 5. The distribution ofξ , the arit
Page 83 and 84: P(x 1i < x) = F(x; a i ) = C(a i )
Page 85 and 86: egards his promises. Markov shows t
Page 87 and 88: other solely and equally possible i
Page 89 and 90: notion of probability and of its re
Page 91 and 92: However, already in the beginning o
Page 93 and 94: the revolution. My main findings we
Page 95 and 96: Nevertheless, Slutsky is not suffic
Page 97 and 98: path that would completely answer h
Page 99 and 100: on political economy as well as wit
Page 101 and 102: scientific merit. Borel was indeed
Page 103 and 104: [3] Already in Kiev Slutsky had bee
Page 105 and 106: different foundation. The difficult
Page 107 and 108: 5. On the criterion of goodness of
Page 109 and 110: --- (1999, in Russian), Slutsky: co
Page 111 and 112: Here also, the author considers the
Page 113 and 114: second, it is not based on assumpti
Page 115 and 116: experimentation and connected with
Page 117 and 118: Russian, and especially of the Sovi
Page 119 and 120: station in England. This book, as h
Page 121 and 122: Uspekhi Matematich. Nauk, vol. 10,
Page 123 and 124: variety and detachment of those lat
Page 125 and 126: 46. On the distribution of the regr
Page 127 and 128: 119. On the Markov method of establ
Page 129 and 130: No lesser difficulties than those e
Page 131: Separate spheres of work considerab
Page 135 and 136: Hier sind, im Allgemeinen, ganz ana
Page 137 and 138: Jedenfalls, glaube ich erwiesen zu
Page 139 and 140: werde ich das ganze Material in kur
Page 141 and 142: considered as the limiting case of
Page 143 and 144: and, inversely,] = m ...1 2 N[ ch h
Page 145 and 146: µ 2 2 = m 2 2 - 2m 2 m 1 2 + m 1 4
Page 147 and 148: (x k - x k+1 ) … (x k - x +) = E(
Page 149 and 150: the thus obtained relations as pert
Page 151 and 152: [1/S(S - 1)(S - 2)][(Si = 1Sx i ) 3
Page 153 and 154: ( N −1)((S − N )(2NS− 3S− 3
Page 155 and 156: µ 5 + 2µ 2 µ 3 = U [S/S] 5 + 2U
Page 157 and 158: case, the same property is true wit
Page 159 and 160: It follows that the question about
Page 161 and 162: then expressed my doubts). And Gned
Page 163 and 164: For Problem 1, formula (7) shows th
Page 165 and 166: Let us calculate now, by means of f
Page 167 and 168: ϕ′1(x)1E(a|x 1 ; x 2 ; …; x n
Page 169 and 170: Theorem 3. If the prior density 3
Page 171 and 172: P( ≤ ≤ |, 1 , 2 , …, s )
Page 173 and 174: 6. A Sensible Choice of Confidence
Page 175 and 176: 0 = A 0 n, = B2, = B2, 0 = C 0 n
Page 177 and 178: Note also that (95),(96), (83),(85)
Page 179 and 180: Γ(n / 2)Γ [( n −1) / 2]k = (1/2
Page 181 and 182: f (x 1 , x 2 , …, x n ) = 1 if x
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and the probability of achieving no
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E = kEµ. (14)In many particular ca
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a = np, b = np 2 = a 2 /n, = a/nand
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with number (2k - 2), we commit an
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(67)which is suitable even without
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" = 1/[1 - e - ], = - ln [1 - (1/
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Such structures are entirely approp
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11. As a result of its historical d
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exaggeration towards a total denial
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kniga 7 - Probability and Statistics 1 - Sheynin, Oscar

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