Fertility model evolution: A survey on mathematical models of age-specific fertility with application to Nepalese and Malaysian data

Abstract

Fertility pattern analysis and modeling to smooth age-specific fertility rates (ASFRs) form a well-established research field that holds particular importance for Asian countries. In developed nations, ASFRs typically display a bimodal skewed fertility curve, whereas, in developing countries, they usually exhibit a unimodal skewed fertility curve that diverges from the normal one. For decades, demographic experts worldwide have been interested in creating models using deterministic and stochastic approaches to represent these fertility curves. In this regard, parametric and non-parametric models have been created, with the latter providing a better fit for ASFR data. This research investigates the evolution of fertility models aimed at smoothing ASFRs. It explores suitable alternative models for countries with fast-declining, unimodal, and skewed fertility curves of ASFRs, such as Nepal and Malaysia. Nepal’s fertility rate is transitioning from a high level toward the replacement rate (2.1) at the year 2021; meanwhile, Malaysia’s fertility rate (1.7) in the year 2021 has dropped below the replacement rate. Given the lack of a universally applicable model for ASFR pattern variation, this study proposes the Kumaraswamy log-logistic distribution as a promising model to represent the ASFRs of Nepal and Malaysia accurately. Various approaches, including the Akaike information criterion, and Bayesian information criterion, are employed to validate the fitting of the proposed model.

Keywords

Age-specific fertility rate / Parametric / Non-parametric / Malaysia / Nepal

Acknowledgments

We would like to express our sincere gratitude to the four anonymous reviewers, the editor, and the editorial team for their invaluable feedback and guidance, which greatly improved the manuscript. The first author is especially grateful to Khwopa Engineering College, Bhaktapur, Nepal, for providing flexible scheduling support, enabling the completion of this research.

Funding

None.

Conflict of interest

The authors declare that they have no competing interests.

Author contributions

Conceptualization: Arjun Kumar Gaire

Formal analysis: Arjun Kumar Gaire

Investigation: All authors

Writing - original draft: Arjun Kumar Gaire

Writing - review & editing: All authors

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data

Data used for this research can be obtained from: NDHS (2022). Demographic and Health Survey 2022: Key Indicators Report. Kathmandu, Nepal: Ministry of Health and Population, Nepal; New ERA; and ICF. Available at: https://www.dhsprogram.com/pubs/pdf/FR379/FR379.pdf

Further disclosure

The article is not presented in any conferences and not submitted in any preprint.

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