A model of the probability of survival from birth

It has recently been shown [1] that the reciprocal of the survivorship function of a life table is very strongly related to a linear combination of the reciprocals of the same function of two or more standard life tables. It follows, therefore, that the mathematical function which describes the reciprocal of ℓ(x) must take the form 1ℓ(x) = 1 + atf1(x, m1, n1, …) + btf2(x, m2, n2, …) + ctf3(x, m3, n3, …) + …, where a, b, c, … are constants for specific life tables and m1, n1, …; m2, n2, …, etc. are constant for all life tables. If ms, ns, … are not constant, then equation (1) will not hold for all values of x. Furthermore, there must be at least two tf functions or else one standard life table would be sufficient to model the reciprocal of ℓ(x) [2]. e parameter equation which meets the above criteria and models the ℓ(x) values of national life tables well is presented along with measures of the goodness of fit. The three parameters are shown to correspond with variations in mortality at young, middle, and old ages.