Generalized probability model for estimating the proportion of the female population at different levels of fertility based on census sampling from a mixed population

The present exercise is an attempt to generalize a probability model referring to the waiting time distribution for conception in a mixed group of fecund females with two varying levels of fecundity, based on a census sample truncated at time T =t from the date of resumption of fecundity following an earlier conception (Biswas, 1975, Sankhya, Series B, 37, Part III). The generalization is made in two aspects, viz. instead of fixed conception rates, time-dependent rates decreasing with the age of the woman have been used. Additionally, unlike the model of Biswas (1975) consisting of two different fecund groups, three different levels of fecundity have been taken into consideration in this paper. Estimates of the proportion of fecund females over time, viz. π_i(t) (i = 1, 2, 3) are attempted by the method of maximum likelihood on the basis of a census sample truncated at time T = t under the generalized set up.