LIFE TABLES. It has long been recognized that there are certain influences which normally affect the duration of life, and that for a large number of individuals of a homogeneous class it is practicable to frame an estimate of their mortality experience. Such estimates at first were based on conjecture rather than on the scientific analysis of observed facts. This appears to have been the case amongst the Romans who had tables for calculating the values of life interests, and no more authentic bases seem to have been discovered until towards the end of the 17th century. The first approximately accurate mortality tables were compiled by Edmund Halley, and were based on the records of baptisms and deaths in the city of Breslau in Germany. About half a century later, De Parcieux published his Essai sur les probabilites de la Duree de la Vie Humaine in which were incorporated several mortality tables which were for many years in general use in France. Meanwhile De Moivre had propounded his well-known theory of the law of mortality, "that the number of lives existing at any age is proportional to the number of years intercepted between the age given and the extremity of old age." As he assumed that 86 was the limiting age, according to his table the number living at any age x was 86—x.
In 1762 the Equitable Society (London) was formed and the business of life assurance began to develop. It was not, however, until the publication in 1771 of a table, prepared by Dr. Price for the records of baptisms and deaths in the parish of All Saints, Northampton, that the science of the construction of mortality tables can be said to have been founded. A revived form of this table, published in 1783, afterwards became famous as The North ampton Table.
There are two main sources from which material for the construction of a mortality table is obtainable, (a) the census returns and death registers of a community, and, (b) the records of assurance companies and other bodies whose operations in volve the duration of life. The statistics relating to the general
population are subject to misstatement of age and other inaccu racies, and it frequently happens that the information is available only in groups of ages, a circumstance which necessitates the subdivision of the group figures into numbers at individual ages The numbers both of the population and the deaths are invariably recorded according to age last birthday. On the other hand, the data obtained from assurance companies are compiled from the individual records of policy-holders who are usually required to furnish evidence of their age before the contract is completed. The numbers living at each age, known as "the exposed to risk," can therefore be scheduled according to nearest age, age last birth day, or any other arrangement that may be convenient.
The functions most usually included in a life table and their relations to one another are .— number of persons surviving at exact age x, =the deaths in the year of age x to x+1 among the per sons who enter on that year, I P.= , the probability of a person aged x living a year, the probability of a person aged x dying in a year, or the rate of mortality at age x, I ex= /. +1, the complete expectation of life, or the total future life-time which, on the average, will be passed through by a person aged exactly x.
Actuaries frequently use tables involving other decremental forces operating in conjunction with mortality, e.g., marriage, widowhood, remarriage and withdrawal.
The construction of a mortality table is carried out by obtain ing from the observation of a number of persons over a limited period the rates of mortality, qz, to which they have been sub ject at each age. The values of having been obtained, the mortality table is formed by selecting a suitable radix, usually taken for convenience as 1 oo,000 at the youngest age in the table, and obtaining successive values of by the formulae /, X qx = d.vp or, since by the formula /x X The other columns of the table can then be completed by means of the appropriate formulae.