Probability model of forward birth interval and its application

In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (μ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and μ through derived model. The estimated values of λ and μ are 1.1051 and 2.841 respectively. The variance of estimated λ and μ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and μ is -0.026.With these estimates the expected frequencies for the distribution and χ = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.