Probabilistic projections of distributions of kin over the life course
Butterick J., Hilton J., Bijak J., Smith PWF., Dodd E.
BACKGROUND Mathematical kinship demography is an expanding area of research. Recent papers have explored the expected number of kin a typical individual should experience. Despite the uncertainty of the future number and distributions of kin, just one paper investigates it. OBJECTIVE We aim to develop a new method for obtaining the probability that a typical population member experiences one or more of some kin at any age through the life course. METHODS Combinatorics, matrix algebra, and convolution theory are combined to find discrete probability distributions of kin number. We propose closed form expressions, illustrating the recursive nature of kin replenishment, using composition of matrix operations. Our model requires as inputs age-specific mortality and fertility. CONCLUSIONS We derive probabilities of kin number for fixed age of kin and over all possible ages of kin. From these the expectation, variance, and other moments of kin number can be found. We demonstrate how kinship structures are conditional on familial events. CONTRIBUTION The paper presents the first analytic approach allowing the projection of a full probability distribution of the number of kin of arbitrary type that a population member has over the life course.