Estimation of the parameters of a type I geometric distribution from truncated observations on conception delays

In connection with the estimation of the average fecundability of a group of women, it has been assumed in the past that the waiting time for a conception follows a type I geometric distribution, and its two parameters have been estimated by the method of moments and the method of maximum likelihood. In a follow-up study, starting with a group of women, there is always the possibility that some women will remain nonpregnant in the limited period of time they are observed, and the problem arises as to how to estimate the same parameters if the follow-up experiment is terminated after a fixed period of time. The present paper deals with this truncation problem, and provides three different methods for estimating the parameters, which are applied to data from the Menstrual and Reproductive History Study at the University of Minnesota. In the last section, an extended model is presented which incorporates the possibility of dropout cases.