References

Booth, Heather (1984). Transforming Gompertz' function for fertility analysis: The development of a standard for the relational Gompertz function. Population Studies 38(3):495-506.

Brass, William (1975). Methods for Estimating Fertility and Mortality from Limited and Defective Data. Chapel Hill NC: Carolina Population Centre.

Coale, Ansley J and DR McNeil (1972). The distribution by age of the frequency of first marriage in a female cohort. Journal of the American Statistical Association 67(340):743-749.

Coale, Ansley J and T James Trussell (1974). Model fertility schedules: Variations in the age structures of childbearing in human populations. Population Index 40(2):185-258.

Gage, Timothy B (2001). Age-specific fecundity of mammalian populations: A test of three mathematical models. Zoo Biology 20(6):487-499.

Gilje E and L Yntema (1970). The shifted Hadwiger fertility function.Working paper number IO70/14. Oslo: Central Bureau of Statistics of Norway.

Hadwiger H (1940). Eine analytische Reprodutionsfunktion fur biologische Gesamtheiten. Skandinavisk Aktuarietidskrift 23(101-113)

Hoem, Jan M, Dan Madsen, Jørgen Løvgreen Nielsen, Else-Marie Ohlsen et al. (1981). Experiments in  modelling recent danish fertility curves. Demography 18(2):231-244.

Retherford, Robert D (1979). The Brass fertility polynomial. Asian and Pacific Census Forum 5(4):15-19,22.

Romaniuk, Anatole (1973). "A three parameter mode for birth projections", Population Studies 27(3):467-478. doi 10.2307/2173766

United Nations (1956). Manual III: Methods for Population Projections by Age and Sex. New York: United Nations.

United Nations, Department of Economic and Social Affairs, Population Division (2013). World Fertility Data 2012 Report No.: POP/DB/Fert/Rev2012. http://www.un.org/esa/population/publications/WFD2012/MainFrame.html external link

Xie, Yu (1990). What is natural fertility? The remodelling of a concept. Population Index 56(4):656-663.

Xie, Yu and Ellen E Pimentel (1992). Age patterns of marital fertility: Revising the Coale-Trussell method. Journal of the American Statistical Association 87(420):977-984.

Further reading

Good introductions to the Coale-Trussell and Relational Gompertz models can be found in the following text books:

Newell, Colin (1988). Methods and Models in Demography. Chichester: John Wiley & Sons – Chapter 14.

Preston, Samuel H, Patrick Heuveline and Michel Guillot (2001). Demography: Measuring and Modelling Population Processes. Oxford: Blackwell – Section 9.3.

On the web

The United Nations Population Division website is a rich source of data on current, past and projected future fertility. Estimates are presented in both their World Population Prospects series, as well as in the occasional World Fertility Data reports.

A detailed exposition of the Relational Gompertz model, and its application to the estimation of fertility from limited or defective data is described on the Tools for Demographic Estimation website (registration required).