Given a set of age nodes \(x_i\) ,\(i=0,\ldots,N\) and a set of fertility rates \(f_i\), \(i=1,\ldots,N\) for the age interval \([x_{i-1},x_i)\). Calculate the cummulative fertility rate \(F_i\) at \(x_i\) $$ F_i=\left\{ \begin{array}{ll} 0 & ,i=0\\ \sum_{k\le i} (x_k-x_{k-1}) f_k & ,i > 0 \end{array}\right. $$ then transform \(F_i\) to \(Y_i\) using the logit function $$ Y_i=\left\{ \begin{array}{ll} Y_0:=\ymin & ,i=0\\ Y_N:=\ymax & ,i=N\\ \mathrm{logit}(F_i/F_N) & ,\mathrm{otherwise} \end{array}\right. $$ Piecewise cubic Hermite interpolation is then used to calculate \(Y(x)\) for all \(x\in[x_0,x_N]\). Cummulative fertility at \(F(x)\) $$ F(x):= \int_{x_0}^x f(a) da $$ is then found by inverting the logit transformation $$ F(x)=\left(\frac{\exp(Y(x))}{1+\exp(Y(x))}\right)F(x_N) $$
By default \(\ymin=-20\) and \(\ymax=12\). These values can be changed using the extrainfo parameters Ymin and Ymax. For example specify the buildmethod HFD:"Ymin=-8","Ymax=10" will set \(\ymin=-8\) and \(\ymax=10\) .