Skip to main content
SpringerLink
Log in

Development of Some Selected Stochastic Models of Human Fertility in India: The Untold Stories

  • Review Article
  • Published:
Journal of the Indian Institute of Science Aims and scope

Abstract

Modeling of any phenomenon requires the knowledge of the subject and the mathematical skill that is required to express the phenomenon in the form of mathematical relationship(s). In the process of model building, the researcher(s) experience several failures and learnings before getting the final model. While large number of final models are developed and published, learnings of model development are seldom documented. Hence, there is a need to bring such articles which could present the learning of model development. Under this premise, the author which has experience of developing stochastic models of human reproduction aims, in this article, to narrate those learnings which he had encountered in the development of large number of models. Since detailed descriptions of those models are already available in publications, the article would skips detail derivations of those models but to provide learnings of the development of the models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bhattacharya BN (1970) On some stochastic models for couple fertility. An Unpublished Thesis Submitted in Banaras Hindu University, Varanasi

  2. Brass W (1958) The distribution of births in human population. Popul Stud 12:51–72

    Google Scholar 

  3. Chiang CL (1968) Introduction to stochastic processes in biostatistics. John Wiley and Sons

    Google Scholar 

  4. Cox DR, Miller HD (1965) The theory of stochastic processes. Methuen and Co.Ltd., London

    Google Scholar 

  5. Dandekar VM (1955) Certain modified forms of binomial and poisson distributions Sankhya. Indian J Stat 15(3):237–250

    Google Scholar 

  6. Feeney G, Ross JA (1984) Analyzing open birth interval distributions. Popul Stud 38:473–478

    CAS  Google Scholar 

  7. Feller W (1966) An introduction to probability theory and its applications. Oliver and Boyd Ltd

    Google Scholar 

  8. Henry L (1953) Fondements theoriques des mesures de la fecondite naturelle. Rev Inst Int Stat 2:135–151

    Google Scholar 

  9. Keyfitz N (1969) Introduction to mathematics of population. Addison-Wesley, Reading

    Google Scholar 

  10. Kumar A, Yadava RC (2015) Usual closed birth interval versus most recent closed birth interval. J Data Sci 13(1):73–94

    CAS  Google Scholar 

  11. Kumar A, Yadava RC (2018) Impact of heterogeneity on closed and open birth intervals. Sankhya B Indian J Stat 2:1

    Google Scholar 

  12. Leridon H (1969) Some comments on an article by K Srinivasan. Popul Stud 23:102

    Google Scholar 

  13. NFHS-2 (1998) National family health survey-2 Report, India

  14. NFHS-3 (2005) National family health survey-2 Report, India

  15. Pandey A, Dwivedi SN, Mishra RN (1990) Distribution of closed birth interval with some biosocial components: a stochastic model and its applications. J Math Sociol 16:89–106

    CAS  Google Scholar 

  16. Pandey A, Singh KK, Singh A (2016) Modelling the proportion of male births under sex preferred stopping rules. Janasamkhya 34:1–8

    Google Scholar 

  17. Pathak KB (1971) A stochastic model for the study of open birth interval—a cohort approach. Sankhya B 33:305–314

    Google Scholar 

  18. Sharma SS (2004) A study on some mathematical models for birth intervals. A Ph.D. Thesis, Banaras Hindu University

  19. Sheps MC, Menken JA (1972) Distribution of birth intervals according to the sampling frame. Theor Popul Biol 3:1–26

    CAS  Google Scholar 

  20. Sheps MC, Menken JA (1973) Mathematical models of conception and birth. University Of Chicago Press, Chicago

    Google Scholar 

  21. Sheps MC, Menken JA, Ridley JC, Linger JW (1970) Truncation effect in closed and open birth interval data. J Am Stat Assoc 65:678–693

    CAS  Google Scholar 

  22. Shukla AK (2006) A study on mathematical models for population dynamics. An Unpublished Thesis Submitted in Banaras Hindu University, Varanasi

  23. Singh SN (1963) Probability models for the variation in the number of births per couple. J Am Stat Assoc 58(303):721–727

    Google Scholar 

  24. Singh SN (1968) A chance mechanism of variation in the number of births per couple. J Am Stat Assoc 63(321):209–213

    Google Scholar 

  25. Singh SN, Bhattacharya BN (1970) A generalized probability distribution for couple fertility. Biometrics 26:33–40

    CAS  Google Scholar 

  26. Singh SN, Bhattacharya BN, Yadava RC (1974) A parity dependent model for number of births and its applications. Sankhya B Indian J Stat 36(1):93–102

    Google Scholar 

  27. Singh SN, Yadava RC (1977) A generalized probability model for an equilibrium birth process. Demogr India 6(1–2):163–173

    Google Scholar 

  28. Singh SN, Yadava RC, Pandey A (1987) On estimating the mean birth interval characteristic of women. Can Stud Popul 14(1):1–8

    Google Scholar 

  29. Singh SN, Yadava RC, Pandey A (1978) A probability model for forward birth interval. Health Popul Perspect Issues 1(4):295–301

    Google Scholar 

  30. Singh SN, Yadava RC, Yadava KNS (1981) A study on the fertility of migrants. Health Popul Perspect Issues 4:959–965

    Google Scholar 

  31. Srinivasan K (1967) Analytical models for two types of birth intervals with applications toindian population. A Ph.D. Thesis, University of Kerala, Trivandrum, India

  32. Srinivasan K (1967) A probability model applicable to the study of inter-live birth intervals and random segments of the same. Popul Stud 21:63–70

    CAS  Google Scholar 

  33. Srinivasan K (1968) A set of analytical models for the study of open birth intervals. Demography 5(1):34–44

    Google Scholar 

  34. Srinivasan K (1980) Birth interval analysis in fertility surveys: an illustrative application to datafrom fiji fertility survey. Scientific Report No. 7. International Statistical Institute, Netherlands

  35. Wolfers D (1968) Determinants of birth intervals and their means. Popul Stud 22:253–262

    CAS  Google Scholar 

  36. Yadava RC, Rai PK (2019) Analyzing variety of birth intervals: a stochastic approach. In: Srinivasa Rao AS, Rao CR (eds) Integrated population biology and modeling Part—B In the handbook of statistics, vol 40. Elsevier, Amsterdam

    Google Scholar 

  37. Yadava, R.C., 2018. Stochastic Modelling of Some Natural Phenomena: A Special Reference to Human Fertility. In: Srinivasa Rao, A.S.R., Rao, C.R. (Eds.), Handbook of Statistics:Integrated Population Biology and Modelling Part A, Vol. 39, Pp. 187–274.

  38. Yadava RC, Bhattacharya M (1985) Estimation of parity progression ratios from closed andopen birth interval data. Centre of Population Studies, Banaras Hindu University, Varanasi, India, Mimeo

    Google Scholar 

  39. Yadava RC, Kumar A, Pratap M (2013) Estimation of parity progression ratios from open and closed birth interval data. J Data Sci 11(3):607–621

    Google Scholar 

  40. Yadava RC, Kumar A, Srivastava U (2013) Sex ratio at birth: a model based approach. Math Soc Sci 65(1):36–39

    Google Scholar 

  41. Yadava RC, Pandey A (1989) On the distribution of straddling birth intervals. Biom J 31(7):855–863

    Google Scholar 

  42. Yadava RC, Pandey A, Saxena NC (1992) Estimation of parity progression ratios from thetruncated distribution of closed and open birth intervals. Math Biosci 110(2):181–190

    CAS  Google Scholar 

  43. Yadava RC, Pandey R, Tiwari AK (2009) On the distribution of menstruating interval. Biodemogr Soc Biol 55(1):1–11

    CAS  Google Scholar 

  44. Yadava RC, Saxena NC (1989) On the estimation of parity progression and instantaneous parity progression ratios. In: Singh SN, Premi MK, Bhatia PS, Ashish B (eds) Population transition in India, vol 1. BR Publishing, Delhi, pp 357–362

    Google Scholar 

  45. Yadava RC, Sharma SS (2004) Closed birth intervals versus most recent closed birth interval. Demogr India 33(2):249–263

    Google Scholar 

  46. Yadava RC, Sharma SS (2007) The distribution of consecutive closed birth intervals in females in Uttar Pradesh. J Biosci 39:185–199

    Google Scholar 

  47. Yadava RC, Srivastava M (1993) On the distribution of births over time in an equilibrium birth process for a female giving specified number of children in a given period. Demogr India 22(2):241–246

    Google Scholar 

  48. Yadava RC, Srivastava M (1998) Extent of infecundity derived from open birth interval data. Demogr India 27(1):205–211

    Google Scholar 

  49. Yadava RC, Tiwari AK (2007) On the pattern of births over time. Demogr India J Indian Assoc Study Popul 36(2):287–302

    Google Scholar 

  50. Yadava RC, Tiwari AK (2010) Symmetry in equilibrium birth process: a mathematical approach. Demogr India 39(2):287–296

    Google Scholar 

Download references

Acknowledgements

The author is extremely thankful to Prof. Piyush Kant Rai, Professor, Department of Statistics for his valuable help and suggestions in the preparation of this article.

Author information

Authors and Affiliations

  1. Former Professor, Department of Statistics, Banaras Hindu University, Varanasi, India

    Ram Chandra Yadava

Authors
  1. Ram Chandra Yadava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ram Chandra Yadava.

Ethics declarations

Conflict of interest

There is no any financial or personal relationship with a third party whose interests could be positively or negatively influenced by this present article’s contents. And this article is written by me as a single author; therefore, I (R.C. Yadava) declare that there is no any conflict of interest in writing this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yadava, R.C. Development of Some Selected Stochastic Models of Human Fertility in India: The Untold Stories. J Indian Inst Sci 102, 1111–1130 (2022). https://doi.org/10.1007/s41745-022-00340-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41745-022-00340-x

Search

Navigation