A discrete-time two-sex age-specific stochastic population program incorporating marriage

Abstract

A discrete-time two-sex stochastic population model is developed. All entities (single males, single females, or couples) are grouped according to their ages, and during a unit time interval, each entity has a choice of several outcomes with fixed conditional probabilities. The model assumes that the number of marriages between men aged x and women aged y is equal to the minimum of the number of men aged x desiring marriage with a woman aged y and the number of women aged y desiring marriage with a man aged x. It follows that if a large excess of males of a11 ages is maintained in the population, the female component grows as a multi-type Galton-Watson process. Under such circumstances, the females have perfect freedom in their choice of marriage partner, and the use of a multi-type Galton-Watson process is very realistic. The same result is true for the male component of the population. Ir there are no males (or females) , no marriages take place, so the model is realistic on this score also. A complex computer program is described, and a detailed numerical example given.

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Pollard, J.H. A discrete-time two-sex age-specific stochastic population program incorporating marriage. Demography 6, 185–221 (1969). https://doi.org/10.2307/2060391

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Keywords

  • Unit Time Interval
  • Positive Part
  • Marriage Rate
  • Single Male
  • Monte Carlo Experiment