Derivation of a Smooth Life Table from a Set of Survivorship Probabilities

There are several situations in which one can obtain estimates of life-table probabilities of survivorship, I(%), but in which one would still want to smooth' these estimates with reference to a model life table. For example, one could calculate a life table directly by converting observed ,m, values into , q, and hence into l(x) values. In other instances, the I (x ) values available may not define a complete life table because some may apply to childhood and some to advanced adult ages (as those obtained from maternal orphanhood data). In the most common situation, one would estimate childhood survivorship probabilities from information on children ever born and children surviving (see chapter 111) and estimate adult suwivorship probabilities from information on spouse survival or on parental survival (see chapter IV), and the age ranges covered by these sets of estimates will not exhaust the 0-85 life-table range. In such cases, both an element of smoothing and some interpolation or extrapolation to obtain missing l(x) values may be necessary. In yet other situations, one may wish to derive complete sets of life-table probabilities of survivorship, 1 (x ), from childhood mortality estimates and conditional survivorship probabilities for adults (such as the probability of surviving from age A to age B, I (B)/l (A )). Conditional probabilities are usually obtained from information on widowhood or orphanhood (see chapter IV) or by the use of some deathdistribution method (see chapter V). The problem one faces in this circumstance is to link the two independent estimates. Again, this linkage is usually accomplished by reference to a model life table. 2. Organization of this chapter