150. On revealing unknown periods of periodic phenomena. TrudyTashkent Geofizich.Observatoria, No. 5 – 6, 1951, pp. 3 – 8. (R)151. On statistical methods of checking manufacturing <strong>and</strong> the quality of the production. ! ! (ProceedingsSecond All-Union Conference on Mathematical <strong>Statistics</strong>). Tashkent, 1948, pp. 24 – 25. (R)152. On straddling by observing short falls <strong>and</strong> shots over the target. Trudy Akad.Artilleriisk. Nauk, 1951. (R)153. On statistical checking the production. Ibidem. (R)154. Comparing hypergeometric, Bernoulli <strong>and</strong> Poisson probabilities. Doklady AN UzbekSSR, No. 10, 1952, pp. 3 – 7. (R)155. On duality theorems for the hypergeometric distribution. Ibidem. (R).156. Same title. Trudy IMM AN Uzbek SSR, No. 11, 1953, pp. 22 – 28. (R)158. Quartile criteria of belonging. Ibidem, pp. 3 – 11. (R)159. On estimating whether a r<strong>and</strong>om sample belongs to a continuous distribution. Ibidem,pp. 12 – 15. (R)9.V.I. Bortkevich (L. von Bortkiewicz).Accidents. ! "#(Brockhaus & Efron Enc. Dict.), halfvol. 40, 1897, pp. 925 – 930In the most general sense, an accident is understood as any unforeseen event causing harmto life or property. Such an underst<strong>and</strong>ing of accidents seems to be too general for therelevant events to be usefully considered under a single head. Special attention, owing totheir importance for both the public health <strong>and</strong> national economy, is due to accidents whosevictims are people engaged as manual laborers in industrial enterprises (accidents du travail,Betriebsunfälle). By dem<strong>and</strong>ing legislative intervention, this group of accidents has latelybecome an independent object of study. There even exists a special International Congresson Accidents. It took place three times (Paris, 1889; Bern, 1891; Milan, 1894), <strong>and</strong>,beginning with this year, it is called Congrès International des Accidents du Travail et desAssurances Sociales.Whether the study of accidents is an aim in itself, or caused by practical considerations(for instance, in connection with the appropriate insurance), the method of examination isalways mostly statistical. This is quite natural since there hardly exists any other domain offacts where the action of the so-called r<strong>and</strong>om causes is felt just as clearly. A propercollection <strong>and</strong> organization of statistics of accidents of the indicated type (of the so-calledoccupational accidents) <strong>and</strong> its correct application is impossible without specifyingbeforeh<strong>and</strong> the concept of occupational accident.It may be defined as a bodily injury unwillingly <strong>and</strong> suddenly caused to a person workingin a certain industrial{in a productive}enterprise by some external process (for example, byfalling down from a high place) or conditions (e.g., by hightened air temperature) duringwork. The suddenness <strong>and</strong> external influence mainly serve as indications for separatingaccidents <strong>and</strong> diseases from each other. Events pathologically quite identical one withanother become, or not become accidents depending on the type <strong>and</strong> the method of the actionof their causes. Lumbago, for example, Márestaing says, should be considered an accidentwhen proven that it was caused suddenly by a single abrupt effort during work. The sameauthor indicates a number of other examples (rupture of a varicose vessel or a muscle, casesof frost-bitten limbs etc) whose attribution to an accident often becomes questionable. This isespecially so when various causes were acting at the same time, some of them purelyexternal, the other ones intrinsic, as a certain predisposition.
No lesser difficulties than those encountered by medical examination are met with whendiscerning those economic indicators that characterize the notion of occupational accident.Usually it is comparatively easy to decide whether the victim of the accident was engaged inthe industrial enterprise; however, his relation with it (more precisely, with its owner) couldwell be understood in different ways. And it is much more often doubtful whether he hadindeed been working at the moment of the accident. It is sometimes hardly possible toascertain when does a certain man begin, <strong>and</strong> end his occupational activities. Especiallydifficult are accidents taking place en route, for instance to, or from the enterprise. Anaccident occurring during a break can also cause doubt. No general solution exists for suchcases. It may be stated about each of them that they constitute a quaestio facti.The definition above provides a guiding principle for solving such problems, but even onlyin principle the concept of occupational accident seems to be questionable. Some authorsfollow the indications stated above, others underst<strong>and</strong> that concept in a narrower sensedem<strong>and</strong>ing that there exist a causal relation between a given accident <strong>and</strong> the victim’s kind ofwork. According to the latter interpretation, an occupational accident may be recognized assuch only when the danger, that brought it about, is exclusively, or in the highest measure (ascompared with the conditions of ordinary life) peculiar to the kind of work of the victim.From that viewpoint, an employee, sent by the owner on an err<strong>and</strong>, even concerningbusiness, <strong>and</strong> run over by a horse-car, is not a victim of an occupational accident. The theoryof occupational risk based on that point of view considerably narrows the domain of theconcept of occupational accident, <strong>and</strong>, therefore, of the sphere of the ensuing legalconsequences (payment of recompense to victim <strong>and</strong> his family on the strength of contract orlaw).The issue of whether the theory is true is connected with the law current in force <strong>and</strong>cannot therefore be solved independently. German laws concerning insurance againstaccidents provide no definite answer to that question <strong>and</strong> the practice of theReichsversicherungsamt, the supreme legal instance on that kind of insurance, revealsnumerous examples of conflicting decisions: first, they recognize the theory of occupationalrisk, then, they reject it as discordant with the will of the lawgiver.Somewhat complete statistical data on accidents exist in those states which introducedpertinent compulsory insurance of considerable groups of the population. To these belongGermany <strong>and</strong> Austria. Special investigations of accidents were also made in other countries,for instance in Switzerl<strong>and</strong> <strong>and</strong> France, <strong>and</strong> the compiled information deserves attention allby itself 1 . However, the probability of leaving accidents out is apparently lower wheninsurance is compulsory. Scientifically <strong>and</strong> practically important are, in addition, not theabsolute, but rather the relative number of accidents, – the ratio of their absolute number tothe number of people exposed to the danger of accidents. Consequently, we ought to knowhow many people are engaged in each branch of industry. And it is very desirable <strong>and</strong> almostnecessary that the information on those exposed to the danger, <strong>and</strong> on the actual victimsissues from the same source; otherwise, disparity in the counting of the same individuals orof those belonging to one <strong>and</strong> the same category will easily occur. This condition can best befulfilled for statistics connected with insurance, <strong>and</strong>, because of the circumstances describedabove, we ought to restrict our attention to the results recorded in German <strong>and</strong> Austrianstatistics.In 1894, in the German industrial associations established for insuring against accidents(gewerbliche Berufsgenossenschaften) having 5.2 mln insured members, there were morethan 190 thous<strong>and</strong> accidents, <strong>and</strong>, in the similar l<strong>and</strong>wirthschaftlicheBerufsgenossenschaften, 12.3 mln <strong>and</strong> about 70 thous<strong>and</strong>, respectively. To these, about 23thous<strong>and</strong> industrial accidents in German enterprises managed by the state, the provinces <strong>and</strong>the communities (0.7 mln insured) should be added.
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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
- Page 77 and 78: x1+ Lp n (x) x1− Lx1+ Lf(t)dt < x
- Page 79 and 80: |(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
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- 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
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- Page 99 and 100: on political economy as well as wit
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- 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
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- Page 117 and 118: Russian, and especially of the Sovi
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- Page 121 and 122: Uspekhi Matematich. Nauk, vol. 10,
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- Page 125 and 126: 46. On the distribution of the regr
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- Page 133 and 134: 10. Anderson, O. Letters to Karl Pe
- 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
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- Page 173 and 174: 6. A Sensible Choice of Confidence
- Page 175 and 176: 0 = A 0 n, = B2, = B2, 0 = C 0 n
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Γ(n / 2)Γ [( n −1) / 2]k = (1/2
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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