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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

annuities will certainly gain pr**of**it. Several authors mentioned the practice,possibly justified by intuitive stochastic reasoning, **of** insuring a number **of**healthy infants cf. § 3.2.3.In the same year, De Witt (Hendriks 1853, p. 109) calculated the cost **of**annuity on several lives (an annuity that should be paid out until the death **of**the 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 table**of** 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 S**of**onea (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 **of**the 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 means**of** elementary stochastic considerations. Petty called the new disciplinepolitical arithmetic and its aims were to study from a socio-economic point18