Impact of heterogeneity on closed and open birth interval

In the study of human fertility, the models of random length of intervals have been found to be useful in studying the dynamics of birth intervals in a better fashion and estimating certain fertility parameters of interest. Vast literature is available where modelling for duration between $i^{th}$ and $(i + 1)^{th}$ births has been done. Apart from other considerations these models assume that consecutive birth intervals are independently distributed. This assumption may be quite reasonable if the population of females is homogeneous with respect to fertility parameters involved in the model. However, if population is heterogeneous with respect to these parameters, then the consecutive intervals are likely to be dependent. In this paper, the behaviour of closed and open birth intervals under the condition of heterogeneity in the population with respect to certain fertility parameters is investigated.