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.
Ajay Shankar Singh,
Human Fertility Behavior Through Birth Interval Models: Overview, American Journal of Theoretical and Applied Statistics.
Vol. 5, No. 3,
2016, pp. 132-137.
Freedman, R., Expected family size and family size value in West Germany, Population Studies, 13; 136, 159, 1959.
Lenski, G., The religious factor, Anchor Books, Doubleday, New York, USA, 1963.
Goldberg, D., Some observations on recent changes in American fertility based on sample survey data, Eugenics Quarterly, 14(4), 255, 1967.
Gini, C., Premieres researches sur la fecundabilite de la femme, Proceedings of the International Mathematics Congress, Toronto, 889-892, 1924.
Sheps, M. C., Pregnancy wastage as a factor in the analysis of fertility data, Demography, 1, 111-118, 1964.
Singh, S. N., Some probability distributions utilized in human fertility, Seminar volume in statistics, BHU, Varanasi, India, p. 74, 1966.
Srinivasan, K., The open birth interval as an index of fertility, Journal of Family Welfare, 13(2), 40, 1966.
Sheps, M. C., Menken, J. A., Ridley, J. C. and Ligner, J. W., Truncation effect in closed birth interval and open birth interval data, Journal of American Statistical Association, 65, 678, 1970.
Singh, S. N. and Yadav, R. C., On the distribution of open birth interval. Paper presented at the International Seminar on Problem of Fertility Control in India, Annamali University, Annamali Nagar, India, 1977.
Singh, S. N., R. C. Yadav, R. C. and Pandey, A., On a generalized distribution of open birth interval regardless of parity, Journal of Scientific Research, BHU, India, 1979.
Pandey, A., A study of some probability models for birth intervals, Ph. D. Thesis, Banaras Hindu University, India, 1981.
Singh, S. N., Yadav, R. C. and Chakrabarty, K. C., A parity dependent model for open birth interval, Sankhya, 44 (2), 212, 1982.
Mishra, R. N., Some stochastic models and their utility to describe birth interval data, Ph. D. Thesis, Banaras Hindu University, India, 1983.
Bhattacharya, B. N., Pandey, C. M. and Singh, K. K., Model for closed birth interval and some social factors, Janasankhya, 6 (1); 57, 1988.
Singh, U., Fertility analysis through birth interval models, unpublished Ph. D. Thesis, Banaras Hindu University, Varanasi, India, 1989.
Singh, A. S., Some analytical models for human fertility and their applications, unpublished Ph. D. Thesis, Institute of Medical Sciences, BHU, Varanasi, India, 1992.
Mturi, A. J., The determinants of birth intervals among non contracepting Tanzanin women, African Population Studies, 12(2), 1997.
Rama Rao S., John T. and Ian A., Correlates of inter birth intervals: Implications of optional birth spacing strategies in Mozambique, Population Council, 1-17, 2006.
Singh S. N., Singh S. N. and Narendra R. K., Demographic and socio-economic determinants of birth interval dynamics in Manipur: A survival analysis, Online Journal of Health and Allied Sciences, 9(4), 2011.
Yadav R. C., Kumar, A. and Pratap, M., Estimation of parity progression ratios from open and closed birth interval, Journal of Data Science, 11, 607-621, 2013.
Singh, A. S., Stochastic model for estimation of fecundability in between two successive live births (Closed Birth Interval), Presented in 3rd International Science Congress, India, Published in Recent Jr. Research Sciences, 3 (ISC-2013), 1-3, 2014.
Singh Ajay Shankar, Probability model for forward birth interval and its application, American Jr. of Theoretical and Applied Statistics, 3(6), 223-227, 2014.
Singh Ajay Shankar, Probability model for human fertility behavior: Straddling birth interval under realistic assumptions, American Jr. of Theoretical and Applied Statistics, 4 (6), 576-580, 2015.
Singh, Ajay S., Statistical estimation techniques and its applications in research, American Journal of Mathematics and Mathematical Sciences, Volume 2, No. 1, p. 7-12, 2013.
Singh A. S., Maximum Likelihood estimation (MLE) technique and its applications in applied and scientific research, Research Dimension, Vol. 3, Issue: IV, pp. 1-4. 2013.
Singh, S. N., Pandey, A. and Mishra, R. N., A generalized probability distribution for open birth interval, The Aligarh Journal of Statistics, 1 (2), p. 183, 1981.
Bongarts, J. and Potter, R. G. Fertility, Biology and Behavior; An analysis of the proximate determinants, Academic Press, new York, USA, 1983.
Srivastava, P. K., Ph. D. (Statistics-Preventive and Social Medicine) unpublished thesis, Institute of Medical Sciences, Banaras Hindu University, India, 1992.
Bhardwaj, S. D., Ph. D. (Statistics-Preventive and Social Medicine) unpublished thesis, Institute of Medical Sciences, Thesis, Banaras Hindu University, India, 1992.