On Modification of the Distribution of Number of Conceptions in an Equilibrium Birth Process

Abstract

The equilibrium birth process assumes that, at the start of the observation period, not all females are exposed to conception, as some may already be pregnant or experiencing postpartum amenorrhea. However, existing models of the equilibrium birth process do not explicitly incorporate the underlying causes of this temporary sterility. The present paper proposes a modified probability model for the number of conceptions in an equilibrium birth process, incorporating the condition that, at the start of the observational period, some females are temporarily sterile due to pregnancy or postpartum amenorrhea. The proposed model is illustrated using four observed birth distributions. It enables estimation of the proportion of temporarily sterile females at the start of the observational period and permits separate estimation of the proportions experiencing temporary sterility due to pregnancy leading to complete conception, pregnancy resulting in foetal loss, and postpartum amenorrhea following either complete or incomplete conception. Furthermore, indirect estimates of the non-susceptibility periods associated with the two types of pregnancy terminations and the probability of a complete conception were obtained for females corresponding to these distributions.