Modeling Human Fertility Using Variance-adjusted Logistic Family of Distributions

Abstract. With changes in the fertility patterns, the earlier developed demographic models fall short in imitating the changes that occur with respect to both time and geographic locations. Models providing a good fit for the classical fertility patterns prove to be inadequate in case of distorted patterns, whereas those useful for distorted data prove to be inefficient and can have poor predictive performance for traditional curves. In this paper, a logistic distribution is taken as a base and new models are proposed for modelling these gradual changes in the age-specific fertility rates. The work consists of differentiating between the pre-modal and the post-modal variability and explores Bayesian techniques to deal with such problems. To show the relevance of the models in current scenario, the real life age-specific fertility rate data of three countries, namely Denmark, India, and Ireland, having different age-specific fertility rate shapes for different years are considered and the posterior samples are generated for further analysis using the Metropolis algorithm. The proposed models are found compatible and satisfactory results are obtained for their respective usages. Finally, the proposed models are compared using some model comparison tools and the best among the proposed models is suggested.

Keywords: Age-specific fertility rate modeling, Bayes information criterion, bimodality, logistic distribution, Metropolis algorithm, predictive loss criterion, prior distribution.

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Recommended citation: Singh, S., Gupta, A., & Upadhyay, S. K. (2025). "Modeling Human Fertility Using Variance-Adjusted Logistic Family of Distributions." American Journal of Mathematical and Management Sciences. 1-24.
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