First Investigations on the Fecundability of a Woman

Abstract

For the Gini Index, Gini’s “approximate measure of the mean fecundability of primipares who had their child in the months of marriage from x + 9 to x + y + 9,” we may write

$$F_G = \frac{{n_{x + 9} - n_{x + y + 10} }}{{\sum\limits_{x + 9}^{x + y + 9} {n_i } }} = \frac{{n_1 - n_{y + 1} }}{{\sum\limits_1^y {n_i } }},$$

where n _i are births in the i’ th, and n _i births in the (i + 9)’th month of exposure. If fecundity differs among women but for each woman is constant over time, the Index has as its limiting value the arithmetic mean fecundability of the non-sterile population N*. This is seen by noting that as y approaches infinity, n_y+1→0 and $\sum\limits_1^y {n_i \to N^* }.$

Proceedings of the International Mathematical Congress (Toronto) 2: 889–892. Translated by David Smith.