The modeling of fertility curves has attracted the demographers for many years. Fertility modeling is main concerned for studying the reproductivity. The modeling of fertility curves by theoretical distribution has been used to describe reproductive patterns of women in childbearing age.

Various types of models have been proposed in literature to capture the fertility patterns. This paper presents the application of Hadwiger function (HWF) model on age specific fertility rates (ASFRs) in Pakistan. The mathematical HWF model describes the fertility curves with more traditional distributions. The important characteristic of  this model is that it estimates three demographic parameters; namely, the total fertility, mean age and modal age of the mothers. The application of HWF model provides meaningful demographic interpretation of its parameters.

In this paper, we fit the HWF model on ASFR of Pakistan during the period 1985-2005. This paper briefly explains the application of HWF and to estimate and interpret the model parameters. The accuracy of fitted HWF model on fertility rates is also determined by root mean square error (RMSE).

Hadwiger function, fertility pattern, modeling, age specific fertility rates.

Received: September 6, 2022; Accepted: November 5, 2022; Published: December 6, 2022

How to cite this article: Hira Fatima Waseem and Farah Yasmeen, Modeling age specific fertility rates of Pakistan with Hadwiger function model, JP Journal of Biostatistics 22 (2022), 1-9. http://dx.doi.org/10.17654/0973514322025

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] J. A. Nasir, M. H. Tahir and M. Riaz, Measuring and modeling the fertility profile of indigenous people in Pakistan: a study of the Arians, Pakistan Journal of Commerce and Social Science 4(2) (2010), 132-146.
[2] World Bank, Fertility decline in Pakistan 1980-2006: a case study, Washington, D.C., USA: The World Bank, Working Paper No. 63071, 2010.
[3] A. Hakim and N. Mahmood, Factors affecting fertility in Pakistan, The Pakistan Development Review 33(4) (1994), 685-709.
[4] Z. A. Sathar, The much-awaited fertility decline in Pakistan: wishful thinking or reality? International Family Planning Perspectives 19 (1993), 142-146.
[5] Z. A. Sathar and J. B. Casterline, The onset of fertility transition in Pakistan, Population and Development Review 24 (1998), 773-796.
[6] M. Zakria and F. Muhammad, Forecasting the population of Pakistan using ARIMA models, Pakistan Journal of Agricultural Sciences 46(3) (2009), 214-223.
[7] H. Hadwiger, Eineanalytische Reproduktions function fürbiologische Gesamtheiten, Scand. Actuar. J. 1940(3-4) (1940), 101-113.
[8] J. M. Hoem, Two papers on analytic graduation, Working Papers from the Central Bureau of Statistics of Norway, IO 74/17, 1974.
[9] J. M. Hoem, D. Madien, J. L. Nielsen, E. M. Ohlsen, H. O. Hansen and B. Rennermalm, Experiments in modelling recent Danish fertility curves, Demography 18(2) (1981), 231-244.
[10] E. Gilje, Fitting curves to age-specific fertility rates: some examples, Statistical Review of the Swedish National Central Bureau of Statistics 3(7) (1969), 118-134.
[11] M. R. Islam and M. K Ali, Mathematical modeling of age specific fertility rates and study the reproductivity in the rural area of Bangladesh during 1980-1998, Pakistan J. Statist. 20(3) (2004), 379-392.
[12] M. Vähi, Fertility modeling, Papers on Anthropology 26(1) (2017), 107-114.
[13] J. A. Nasir, M. Akhtar and M. H. Tahir, Reproductivity and age specific fertility rates in Pakistan after 1981, Pakistan J. Statist. 25(3) (2009), 251-263.
[14] M. Zakria, M. Yaseen, F. Muhammad and S. Mahmood, Modelling fertility patterns of Pakistan during 1984-2007, Pakistan J. Statist. 29(4) (2013), 479-486.
[15] F. Yasmeen and Z. Mahmood, Forecasting age-specific fertility rates of Pakistan using functional time series model, Proceedings of 12th Islamic Countries Conference on Statistical Sciences (ISOSS) at Doha, Qatar, Vol. 23, 2012, pp. 669-674.
[16] R. J. Hyndman and M. S. Ullah, Robust forecasting of mortality and fertility rates: a functional data approach, Comput. Statist. Data Anal. 51(10) (2007), 4942-4956.
[17] T. Chandola, D. A. Coleman and R. W. Hiorns, Recent European fertility patterns: fitting curves to ‘distorted’ distributions, Population Studies 53(3) (1999), 317-329.
[18] R. Hussain and A. Bittles, Consanguineous marriage and differentials in age at marriage, contraceptive use and fertility in Pakistan, Journal of Biosocial Science 31(1) (1999), 121-138.