Volume 54 - Article 9 | Pages 263–308  

Probabilistic projections of distributions of kin over the life course

By Joe Butterick, Jason Hilton, Jakub Bijak, Peter W F Smith, Erengul Dodd

Abstract

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.

Author’s Affiliation

• Joe Butterick - University of Southampton, United Kingdom EMAIL
• Jason Hilton - University of Southampton, United Kingdom EMAIL
• Jakub Bijak - University of Oxford, United Kingdom EMAIL
• Peter W F Smith - University of Southampton, United Kingdom EMAIL
• Erengul Dodd - University of Southampton, United Kingdom EMAIL

Other articles by the same author/authors in Demographic Research

Integrating uncertainty in time series population forecasts: An illustration using a simple projection model
Volume 29 - Article 43

Reforging the Wedding Ring: Exploring a Semi-Artificial Model of Population for the United Kingdom with Gaussian process emulators
Volume 29 - Article 27

Investigating the application of generalized additive models to discrete-time event history analysis for birth events
Volume 47 - Article 22

Editorial: The past, present, and future of Demographic Research
Volume 41 - Article 41

Editorial: P-values, theory, replicability, and rigour
Volume 41 - Article 32

Quantifying paradigm change in demography
Volume 30 - Article 32

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