Fit fertility rates with a Beta density $$ f(x)=R \frac{\Gamma(A+B)}{\Gamma(A)\Gamma(B)}(\beta-\alpha)^{-(A+B-1)} (x-\alpha)^{A-1} (\beta-x)^{B-1},\quad \alpha< x< \beta $$ where \begin{eqnarray} B&=&\left[\frac{(\mean-\alpha)(\beta-\mean)}{\var}-1\right]\frac{\beta-\mean}{\beta-\alpha}\\ A&=&B\,\frac{\mean-\alpha}{\beta-\mean} \end{eqnarray} and \(\mean\) is the mean and \(\var\) is the variance. The parameters \(R\), \(\alpha\), \(\beta\), \(\mean\), and \(\var\) are chosen to minimize the square of the absolute error in fertility rates.