AccScience Publishing / GHES / Online First / DOI: 10.36922/ghes.4219
Submit to GHES
Cite this article
17
Download
464
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
ORIGINAL RESEARCH ARTICLE

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

Arjun Kumar Gaire1,2* ,  Yogendra Bahadur Gurung1 ,  Tara Prasad Bhusal3
Show Less
1 Central Department of Population Studies, Tribhuvan University, Kirtipur, Nepal
2 Department of Science and Humanities, Khwopa Engineering College, Purbanchal University, Bhaktapur, Nepal
3 Central Department of Economics, Tribhuvan University, Kirtipur, Nepal
GHES, 4219 https://doi.org/10.36922/ghes.4219
Submitted: 11 July 2024 | Accepted: 14 September 2024 | Published: 11 November 2024
© 2024 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
Download PDF
Cite
XML
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
Funding
None.
Conflict of interest
The authors declare that they have no competing interests.
References
  1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6):716-723. https://doi.org/10.1109/TAC.1974.1100705

 

  1. Aryal, G.R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and Probability, 2(1):11-20. https://doi.org/10.12785/jsap/020102

 

  1. Asili, S., Rezaei, S., & Najjar, L. (2014). Using skew-logistic probability density function as a model for age-specific fertility rate pattern. BioMed Research International, 2014:790294. https://doi.org/10.1155/2014/790294

 

  1. Beer, J.D. (2011). A new relational method for smoothing and projecting age-specific fertility rates: TOPALS. Demographic Research, 24:409-454. https://doi.org/10.4054/DemRes.2011.24.18

 

  1. Bozik, J.E., & Bell, W.R. (1987). Forecasting Age Specific Fertility Using Principal Components. Washington DC, USA: US Bureau of the Census, p.396-401.

 

  1. Brass, W. (1974). Perspectives in population prediction: Illustrated by the statistics of England and Wales. Journal of the Royal Statistical Society: Series A (General), 137(4):532-570. https://doi.org/10.2307/2344713

 

  1. Chandola, T., Coleman, D.A., & Hiorns, R.W. (1999). Recent European fertility patterns: Fitting curves to ‘distorted’ distributions. Population Studies, 53(3):317-329. https://doi.org/10.1080/00324720308089

 

  1. Chandola, T., Coleman, D.A., & Hiorns, R.W. (2002). Heterogeneous fertility patterns in the English-speaking world. Results from Australia, Canada, New Zealand and the United States. Population Studies, 56(2):181-200.

 

  1. De-Santana, T.V.F., Ortega, E.M., Cordeiro, G.M., & Silva, G.O. (2012). The Kumaraswamy-log-logistic distribution. Journal of Statistical Theory and Applications, 11(3):265-291.

 

  1. Gaire, A.K. (2023). Skew Lomax distribution: Parameter estimation, its properties, and applications. Journal of Science and Engineering, 10(1):1-11. https://doi.org/10.3126/jsce.v10i1.61011

 

  1. Gaire, A.K., & Aryal, R. (2015). Inverse Gaussian model to describe the distribution of age specific fertility rates of Nepal. Journal of Institute of Science and Technology. 20(2):80-83. https://doi.org/10.3126/jist.v20i2.13954

 

  1. Gaire, A.K., & Gurung, Y.B. (2024a). Rayleigh generated log-logistic distribution: Properties and application. Istatistik Journal of the Turkish Statistical Association, 15(1).

 

  1. Gaire, A.K., & Gurung, Y.B. (2024b). Skew log-logistic distribution: Properties and application. Statistics in Transition New Series, 25(1):43-62. https://doi.org/10.59170/stattrans-2024-003

 

  1. Gaire, A.K., Gurung, Y.B., & Bhusal, T P. (2024). Age at first marriage of Nepalese women: A statistical analysis (status, differential, determinants, and distributional pattern). Journal of Population and Social Studies, 32(1):308-328. https://doi.org/10.25133/JPSSv322024.019

 

  1. Gaire, A.K., Gurung, Y.B., & Bhusal, T.P. (2023). Stochastic modeling of age at menopause for Nepalese women and development of menopausal life table. Global Health Economics and Sustainability, 1(2):1239. https://doi.org/10.36922/ghes.1239

 

  1. Gaire, A.K., Thapa G.B., & Samir, K.C. (2019). Preliminary Results of Skew Log-Logistic Distribution, Properties, and Application. In: Proceeding of the 2nd International Conference on Earthquake Engineering and Post Disaster Reconstruction Planning (ICEE-PDRP-2019). Bhaktapur, Nepal, p.37-43. Available from: https://icee-pdrp.khwopaconference.com/themes/icee_pdrp_v3/ downloads/2nd_conf_final_proceeding.pdf [Last accessed on 2024 Jul 07].

 

  1. Gaire, A.K., Thapa, G.B., & Samir, K.C. (2022). Mathematical modeling of age-specific fertility rates of Nepali mothers. Pakistan Journal of Statistics and Operation Research, 18(2):417-426. https://doi.org/10.18187/pjsor.v18i2.3319

 

  1. Gayawan, E., & Ipinyomi, R.A. (2009). A comparison of Akaike, Schwarz and R square criteria for model selection using some fertility models. Australian Journal of Basic and Applied Sciences, 3(4):3524-3530.

 

  1. Gayawan, E., Adebayo, S.B., Ipinyomi, R.A., & Oyejola, B.A. (2010). Modeling fertility curves in Africa. Demographic Research, 22:211-236. https://doi.org/10.4054/DemRes.2010.22.10

 

  1. Gilje, E. (1969). Fitting curves to age-specific fertility rates: Some examples. Statistical Review of the Swedish National Central Bureau of Statistics, 3(7):118-134.

 

  1. Gilje, E., & Yntema, L. (1971). The shifted Hadwiger fertility function. Scandinavian Actuarial Journal, 1971(1-2):4-13. https://doi.org/10.1080/03461238.1971.10404657

 

  1. Hadwiger, H. (1940). Eine analytische Reproduktionsfunktion für biologische Gesamtheiten. Scandinavian Actuarial Journal, 1940(3-4): 101-113.

 

  1. Hoem, J.M., & Berge, E. (1975). Some problems in Hadwiger fertility graduation. Scandinavian Actuarial Journal, 1975(3):129-144. https://doi.org/10.1080/03461238.1975.10405091

 

  1. Hoem, J.M., Berge, E., & Holmbeck, B. (1976). Four Papers on the Analytic Graduation of Fertility Curves. Oslo, Norway: Central Bureau of Statistics of Norway.

 

  1. Hoem, J.M., Madien, D., Nielsen, J.L., Ohlsen, E.M., Hansen, H.O., & Rennermalm, B. (1981). Experiments in modelling recent Danish fertility curves. Demography, 18(2):231-244.

 

  1. Islam, M.R., & Ali, M.K. (2004). Mathematical modeling of age-specific fertility rates and study of the productivity in the rural area of Bangladesh during 1980-1998. Pakistan Journal of Statistics, 20(3):379-392.

 

  1. Islam, R. (2009). Mathematical modeling of age-specific marital fertility rates of Bangladesh. Research Journal of Mathematics and Statistics, 1(1):19-22.

 

  1. Islam, R. (2011). Modeling of age-specific fertility rates of Jakarta in Indonesia: A polynomial model approach. International Journal of Scientific & Engineering Research, 2(11):1-5.

 

  1. Jeha, D., Usta, I., Ghulmiyyah, L., & Nassar, A. (2015). A review of the risks and consequences of adolescent pregnancy. Journal of Neonatal-Perinatal Medicine, 8(1):1-8. https://doi.org/10.3233/npm-15814038

 

  1. Kostaki, A., Moguerza, J.M., Olivares, A., & Psarakis, S. (2009). Graduating the age-specific fertility pattern using support vector machines. Demographic Research, 20:599-622. https://doi.org/10.4054/DemRes.2009.20.25

 

  1. Liu, Y., Gerland, P., Spoorenberg, T., Kantorova, V., & Andreev, K. (2011). Graduation Methods to Derive age-specific Fertility Rates from Abridged Data: A Comparison of 10 Methods Using HFD Data. Presentation at the First HFD Symposium, MPIDR, Rostock, Germany.

 

  1. Mazzuco, S., & Scarpa, B. (2011). Fitting Age-specific Fertility Rates by a Skew-symmetric Probability Density Function. Working Paper Series, No. 10. Italy: The University of Padova.

 

  1. Mishra, R., Singh, K.K., & Singh, A. (2017). A model for age-specific fertility rate pattern of India using skew-logistic distribution function. American Journal of Theoretical and Applied Statistics, 6(1):32-37. https://doi.org/10.11648/j.ajtas.20170601.14

 

  1. Murphy, E.M., & Nagnur, D.N. (1972). A Gompertz fit that fits: Applications to Canadian fertility patterns. Demography, 9(1):35-50.

 

  1. (2017). Nepal Demographic and Health Survey 2016: Key Indicators. Kathmandu, Nepal: Ministry of Health and Population, New ERA and ICF. Available from: https://www. dhsprogram.com/pubs/pdf/fr336/fr336.pdf [Last accessed on 2024 Jul 07].

 

  1. (2022). Demographic and Health Survey 2022: Key Indicators Report. Kathmandu, Nepal: Ministry of Health and Population, New ERA and ICF. Available from: https://dhsprogram.com/pubs/pdf/FR379/FR379.pdf [Last accessed on 2024 Jul 07].

 

  1. (2023). Preliminary Report: Malaysian Demographic and Health Survey 2022. Kuala Lumpur, Malaysia: National Population and Family Development Board. Available from: https://www.dosm.gov.my/portal-main/release-content/ vital-statistics-2024 [Last accessed on 2024 Jul 07].

 

  1. Pasupuleti, S.S., & Pathak, P. (2011). Special form of Gompertz model and its application. Genus, 66(2):95-125. https://doi.org/10.4402/genus-276

 

  1. Peristera, P., & Kostaki, A. (2007). Modeling fertility in modern populations. Demographic Research, 16:141-194. https://doi.org/10.4054/DemRes.2007.16.6

 

  1. Salomon, J.A., & Murray, C.J. (2001). Modeling HIV/AIDS epidemics in sub-Saharan Africa using seroprevalence data from antenatal clinics. Bulletin of the World Health Organization, 79(7):596-607.

 

  1. Santos, N.L.C., Costa, M.C.O., Amaral, M.T.R., Vieira, G.O., Bacelar, E.B., & De-Almeida, A.H.V. (2014). Teenage pregnancy: Analysis of risk factors for low birth weight, prematurity and cesarean delivery. Science and Public Health, 19(3):719-726. https://doi.org/10.1590/1413-81232014193.18352013

 

  1. Schmertmann, C.P. (2003). A system of model fertility schedules with graphically intuitive parameters. Demographic Research, 9:81-110. https://doi.org/10.4054/DemRes.2003.9.5

 

  1. Schmertmann, C.P., & Caetano, A.J. (1999). Estimating parametric fertility models with open birth interval data. Demographic Research, 1(4):1-27. https://doi.org/10.4054/DemRes.1999.1.5

 

  1. Singh, B.P., Gupta, K., & Singh, K.K. (2015). Analysis of fertility pattern through mathematical curves. American Journal of Theoretical and Applied Statistics, 4(2):64-70. https://doi.org/10.11648/j.ajtas.20150402.14

 

  1. (2018). Global Health Estimates. Deaths by Cause, Age, Sex, Country, and Region, 2000-2016. Geneva: World Health Organization. Available from: https://www.who. int/data/gho/data/themes/mortality-and-global-health-estimates [Last accessed on 2024 Jul 07].
Share
Back to top
Global Health Economics and Sustainability, Electronic ISSN: 2972-4570 Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept