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 ...

annuities will certainly gain profit. Several authors mentioned the practice,possibly justified by intuitive stochastic reasoning, of insuring a number ofhealthy infants cf. § 3.2.3.In the same year, De Witt (Hendriks 1853, p. 109) calculated the cost ofannuity on several lives (an annuity that should be paid out until the death ofthe last person of the group, usually, of a married couple) and thusdetermined the distribution of the maximal term of a series of observations[obeying a uniform law]. Kohli & van der Waerden (1975) described thehistory of life insurance including the work of De Witt and Huygens (§2.2.2).The first estimation of the present worth of life annuities, based on a tableof expectations of life, was made by the Praetorian Prefect Ulpianus (170 –228), see Hendriks (1852) and Greenwood (1940 and 1941 – 1943). Hissources are not known, neither is it clear whether his expectation coincidedwith our present notion, but at least methodologically his table constitutedthe highest achievement of demographic statistics until the 17 th century.Leibniz (MS 1680?/1872) described his considerations about stateinsurance, see Sofonea (1957a). He had not studied insurance as such, butmaintained that the princes should care about the poor, that the societyought to be anxious for each individual etc. Much later Süssmilch (§ 6.2.2)formulated similar ideas.Tontines constituted a special form of mutual insurance. Named after theItalian banker Laurens Tonti, 1630 – 1695 (Hendriks 1863), they, acting as asingle body of participants, distributed the total sums of annuities amongtheir members still alive, so that those, who lived longer, receivedconsiderable moneys. Tontines were neither socially accepted norwidespread on the assumed rationale that they are too selfish andspeculative (Hendriks 1853, p. 116). Nevertheless, they did exist in the 17 thcentury. Euler (1776) proposed flexible tontines with variable ages of theirmembers as well as their initial contributions. Such tontines would thenbecome perpetual bodies rather than remaining only for a few decades inexistence. Apparently for the same reason his proposal had not beenadopted.2.1.4. Population Statistics. The Old Testament (Numbers, Chapter 1)reports on a census of those able to bear arms and, accordingly, the Talmudestimated the population of towns only by the number of soldiers broughtforth [when needed]. In China, in 2238 BC or thereabouts, an estimation ofthe population was attempted and the first census of the warrior caste inEgypt occurred not later than in the 16 th century BC (Fedorovitch 1894, pp.7 – 21). In Europe, even in 15 th century Italy, for all its achievements inaccountancy and mathematics (M. G. Kendall 1960),counting was by complete enumeration and still tended to be a record of asituation rather than a basis for estimation or prediction in an expandingeconomy.Only Graunt (1662) and, to a lesser extent, Petty (1690) can be called thefathers of population statistics. They studied population, economics, andcommerce and discussed the appropriate causes and connections by meansof elementary stochastic considerations. Petty called the new disciplinepolitical arithmetic and its aims were to study from a socio-economic point18

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