A Bayes Study of Human Fertility Curve Using Mixture of Two Weibull Densities

Abstract

The paper considers the use of a mixture of two Weibull densities to represent fertility patterns with a hump or bimodality behaviour, a pattern in fertility that has been noticed by researchers in the last two to three decades. Assuming the births to be distributed as a binomial variate and taking into account the period age-specific fertility rates, the paper relies on the Bayes paradigm to provide the complete posterior analysis. Guided by the results of the proposed mixture of two Weibull densities, the paper then proposes two other mixture models, that is, the mixture of normal and Weibull and the mixture of normal and generalized gamma densities. The Metropolis algorithm with a properly chosen candidate generating density is considered to generate the posterior samples in each case. The unabridged data are used for numerical illustration. Finally, the proposed models are compared to recommend the most appropriate model after establishing the compatibility of the proposed models with the data in hand. The work is, of course, motivated by the earlier studies that overlooked the use of more flexible lifetime models in studying fertility patterns with hump or bimodality and, as such, prompting us to integrate them into our analysis. © The Indian Society for Probability and Statistics (ISPS) 2025.