On a Statistical Model Useful for Demographics: Estimating the Mean Number of Children Ever Born Through the Distribution of Male Births with an Application to Data from India

The connection between male births and fertility can be easily linked with demographic transition and in defining the population distribution. In this context, it is necessary to understand the birth patterns in Indian societies which are governed by some or the other probability distributions. Although child birth is a biological process but it is very much influenced by a number of social, economic, cultural and psychological factors. Numerous demographers have proposed mathematical models to predict the number of male and female births during a given time period taking into consideration the various factors. Traditionally, estimating current levels and future trends of mean number of births is done using various life tables, cohort-component method, time-series analysis, micro-simulations, structural modeling, expert analysis, historical error analysis and also using an appropriate probability model and testing the model on real data. In the present study we developed a model for estimating the mean number of children ever born through the join probability distribution with its application for male births among the females of Uttar Pradesh and Bihar. The reasons of selecting these two states were their huge population and high total fertility rates. The model fits to the data of these two states, therefore it would be a good fit for the other states too, which shows the efficiency and applicability of the model. The applicability of this model has been illustrated on real data obtained from the National Family Health Survey-3 (2005–06). The various estimates of the parameters have been obtained by using the method of moments and suitability of the proposed model has been tested using the ‘goodness of fit’ criteria.