Parametric models of fertility (cont.)
Brass’ fertility polynomial (cont.)
In Brass’ original exposition of the method, s was allowed to vary between 11.5 and 18.5 to generate a range of fertility schedules, although the effect of changing s merely shifts the curve along the x-axis, and does not alter the underlying age pattern of fertility.
On the graph below, use the arrows to see this variety.
It is a property of this polynomial that the mean age of the fertility schedule is s + 13.2 years, and the maximum fertility rate (that is, the mode) occurs at s + 11 years. These, and many other, properties of the Brass polynomial are described and set out by Retherford (1979).