Krishnamoorthy S
Demography. 1979 Feb;16(1):121-9.
Mathematical expressions are developed for certain life cycles when only the age-specific birth and death rates are known. The probability at birth that a woman will have a specified number of children and the expected length of time spent before the first birth, between the first and the last child, and between the last child and the time of the woman's death are shown to be calculable. Expressions for the probability of at least one child outliving the mother and for the expected number of children outliving the mother are also developed and are evaluated for three selected countries with different birth and death rates to show how these life cycles depend on birth and death rates.
当仅知道特定年龄的出生率和死亡率时，就可以针对某些生命周期推导出数学表达式。结果表明，一名女性生育特定数量子女的出生时概率，以及首次生育前、第一个孩子与最后一个孩子之间、最后一个孩子与女性死亡之间所花费的预期时长都是可以计算的。还推导出了至少有一个孩子比母亲长寿的概率表达式以及比母亲长寿的孩子的预期数量表达式，并针对三个具有不同出生率和死亡率的选定国家进行了评估，以展示这些生命周期如何依赖于出生率和死亡率。
