Fertility and replacement: some alternative stochastic models and results for Brazil
The observed joint distribution of births and child deaths for a cohort of women at a given point in time depends on the number of children that would have been born had the family experienced no deaths, the number of child deaths experienced, and the proportion of these deaths that are replaced by a subsequent birth. In this paper we estimate the parameters of the assumed distributions of these three events using a minimum distance estimation model and data from the 1970 Brazilian census. The parameter estimates are shown to be similar to those obtained previously using a maximum likelihood estimation model. When the data are subdivided according to women's years of schooling, estimates of probability of a child death and mean and variance of children born if no deaths decrease while estimates of probability of replacement of a dead child increase as years of schooling increase
Mauskopf, J., & Wallace, T. D. (1984). Fertility and replacement: some alternative stochastic models and results for Brazil. Demography, 21(4), 519-536.