Fertility is one of the responsible factors for the growth of human population. The demographers have given priority to understanding of the determinants of fertility through statistical techniques. Analytical models are suitable and appropriate tools and are widely used for better understanding of the phenomenon of the human fertility behavior. In other words, these models are useful in describing the action and interaction among various factors as well as for predicting the change in fertility behavior. The analytic models play an important role in estimation and interpretation of the fertility behaviors. In this paper, discuss the of birth intervals model based on realistic assumptions of human reproductive process, indirectly incorporating socio-cultural, bio-demographic factors, taboos and also use of contraceptive practices. In these derived models to describe the variation in the length of closed, forward, straddling and open birth interval with the realistic assumption that all the females are not exposed to the risk of conception immediately after the termination of post-partum amenorrhea (PPA) due to some factors or contraceptive practices. In these models, fecundability (λ) has been considered to be constant over the study period. The duration of time from the point of termination of PPA to the state of exposure has been taken as random variable which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameter (λ) through different derived models.