The lengths of the “closed” intervals from the ith to the (i + 1)th birth (Xi ) and of the “open” intervals since the most recent birth (Un ) for women who have had exactly n births have been considered useful indicators of current changes in natality patterns. Particularly, it has been hoped that such data will provide information regarding the p.d.f. of χ i , the corresponding interval that would be observed if there were infinite time for reproduction. Since Xi and Un depend on the convolution of the p.d.f.'s for xj (j = 0, 1, …, i) and on t (the duration of fecund marriage at the time of survey), a set of Xi forms a truncated sample of the corresponding xi . The Un also depend on analogous convolutions and on t. As a result, even given uniform t for all the subjects, a change in the p.d.f. of xi , such as a shift to the right, will not necessarily be reflected in observed data on Xi or Un . This difficulty is not overcome by life table analysis except under highly restrictive assumptions. It ...