Barrett and Marshall Model for conception: A biologically reasonable model for the probability of conception in a particular menstrual cycle, which supposes that the batches of sperm introduced on different days behave without any dependency. The model is
where the Xik are 0,1 variables corresponding to whether there was the intercourse or not on a particular day relative to the estimated day of the ovulation (which is day 0). The parameter pi is interpreted as the probability that the conception would happen following intercourse on the day i only.