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 ...

the ratio of the chances that they be ruined. The stipulated numbers of pointsoccur in 15 and 27 cases and the ratio sought is therefore (5/9) 12 .In 1669, in a correspondence with his brother, Huygens (1895), see Kohli& van der Waerden (1975), discussed stochastic problems connected withmortality and life insurance. Issuing from Graunt’s mortality table (§ 2.1.4),Huygens (pp. 531 – 532) introduced the probable duration of life (but notthe term itself). On p. 537 he specified that expected life ought to be used incalculations of annuities and the former for betting on human lives. Huygensalso showed that the probable duration of life could be determined by meansof the graph (plate between pp. 530 and 531) of the function y = 1 – F(x),where, in modern notation, F(x) was a remaining unknown integraldistribution function with admissible values of the argument being 0 ≤ x ≤100.In the same correspondence Huygens (p. 528) examined the expectedperiod of time during which 40 persons aged 46 will die out; and 2 personsaged 16 will both die. The first problem proved too difficult, but Huygensmight have remarked that the period sought was 40 years (according toGraunt, 86 years was the highest possible age). He mistakenly solved asimilar problem by assuming that the law of mortality was uniform and thatthe number of deaths will decrease with time, but for a distribution,continuous and uniform in some interval, n order statistics will divide it into(n + 1) approximately equal parts and the annual deaths will remain aboutconstant. In the second problem Huygens applied conditional expectation.When solving problems on games of chance, Huygens issued fromexpectations which varied from set to set rather than from constantprobabilities and was compelled to compose and solve difference equations.See also Shoesmith (1986).2.2.3. Newton. Newton left interesting ideas and findings pertaining toprobability, but more important were his philosophical views (K. Pearson1926):Newton’s idea of an omnipresent activating deity, who maintains meanstatistical values, formed the foundation of statistical development throughDerham, Süssmilch, Niewentyt, Price to Quetelet and Florence Nightingale[…]. De Moivre expanded the Newtonian theology and directed statisticsinto the new channel down which it flowed for nearly a century. The causewhich led De Moivre to his Approximatio [1733] or Bayes to his theoremwere more theological and sociological than purely mathematical, and untilone recognizes that the post-Newtonian English mathematicians were moreinfluenced by Newton’s theology than by his mathematics, the history ofscience in the 18 th century – in particular that of the scientists who weremembers of the Royal Society – must remain obscure.On De Moivre see Chapt. 4 and Bayes theorem is a misnomer (§ 5.1).Then, Newton never mentioned mean values. In 1971, answering myquestion on this point, the Editor of his book (1978), E. S. Pearson, stated:From reading [the manuscript of that book] I think I understand what K.P. meant. […] He had stepped ahead of where Newton had to go, by statingthat the laws which give evidence of Design, appear in the stability of the23

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