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Stochastic Processes in Demography and Their Computer Implementation pp 112–176Cite as

Models of Maternity Histories and Age-Specific Birth Rates

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Part of the book series: Biomathematics ((BIOMATHEMATICS,volume 14))

Abstract

At any time point, the size of a population closed to in-and-out migration will increase or decrease, depending on the balance between births and deaths. Consequently, along with the study of mortality discussed in the previous two chapters, the study of fertility, the factors and circumstances underlying the flow of births into a population, has long been of central interest to students of population. In countries in which births are registered according to the age of the mother and estimates of the size of the female population are available by age groups, age-specific birth (fertility) rates are routinely calculated. During the past two decades, however, the investigation of fertility has also been approached through the study of maternity histories, a study that is sometimes referred to as birth interval analysis. With respect to data requirements, the two approaches to investigating fertility are distinct. Period age-specific birth rates provide summary measures of the birth experiences of all women in the childbearing ages during short time periods, consisting of one or more calendar years. Analyzing data on maternity histories, on the other hand, entails following cohorts of women over longer time periods, which may, particularly in the analysis of historical data, include entire reproductive careers, starting with marriage to the onset of physiological sterility.

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References

  • Aitchison, J. and Brown, J.A.C. (1963): The Lognormal Distribution. Cambridge University Press, Cambridge

    Google Scholar 

  • Anderson, T.W. (1958): An Introduction to Multivariate Statistical Analysis. John Wiley and Sons, New York

    MATH  Google Scholar 

  • Bishop, Y.M.M., Fienberg, S.E. and Holland, P.W. (1975): Discrete Multivariate Analysis — Theory and Practice. M.I.T. Press, Cambridge, Mass.

    MATH  Google Scholar 

  • Blackwood, L. (1981): Alaska Native Fertility Trends, 1950–1978. Demography 18:173–178

    Article  Google Scholar 

  • Brass, W. (1958): The Distribution of Births in Human Populations. Population Studies 12:51–72

    Google Scholar 

  • Brass, W. (1960): The Graduation of Fertility Distributions by Polynomial Functions. Population Studies 14:148–162

    Google Scholar 

  • Brass, W. (1978): Population Projections for Planning and Policy. Papers of the East-West Population Institute, # 55. Honolulu, Hawaii

    Google Scholar 

  • Braun, H.I. (1980): Regression — Like Analysis of Birth Interval Sequences. Demography 17:207–221

    Article  Google Scholar 

  • Braun, H.I. and Hoem J.M. (1979): Modelling Cohabitation Birth Intervals in the Current Danish Population. Working Paper No. 24, Laboratory of Actuarial Mathematics, University of Copenhagen

    Google Scholar 

  • Coale, A.J. (1971): Age Patterns of Marriage. Population Studies 25:193–214

    Google Scholar 

  • Coale, A.J. (1972): The Growth and Structure of Human Populations. Princeton University Press, Princeton, New Jersey

    Google Scholar 

  • Coale, A.J. and McNeil, D.R. (1972): The Distribution by Age of the Frequency of First Marriage in a Female Cohort. Journal of the American Statistical Association 67:743–749

    Article  Google Scholar 

  • Coale, A.J. and Trussell, T.J. (1974): Model Fertility Schedules — Variation in the Age-Structure of Childbearing in Human Populations. Population Index 40:185–258

    Article  Google Scholar 

  • Coale, A.J. and Trussell, T.J. (1978): Technical Note — Finding the Two Parameters That Specify a Model Schedule of Marital Fertility. Population Index 44:203–213

    Article  Google Scholar 

  • Curtin, L.R., Frockt, I.J. and Koch, G.G. (1979): A Note on the Analysis of Parity Progression Ratios. Demography 16:481–484

    Article  Google Scholar 

  • Dandekar, K. (1963): Analysis of Birth Intervals of a Set of Indian Women. Eugenics Quarterly 10:73–78

    Google Scholar 

  • de Finetti, B. (1973): La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincar— 7:1–68

    Google Scholar 

  • Farid, S.M. (1973): On the Pattern of Cohort Fertility. Population Studies 27:159–168

    Google Scholar 

  • Feller, W. (1966): An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley and Sons, New York

    MATH  Google Scholar 

  • Feller, W. (1968): An Introduction to Probability Theory and Its Applications. Vol. I, Third Edition. John Wiley and Sons, New York

    MATH  Google Scholar 

  • Galambos, J. (1978): The Asymptotic Theory of Extreme Order Statistics. John Wiley and Sons, New York

    MATH  Google Scholar 

  • Galton, F. (1879): The Geometric Mean in Vital and Social Statistics. Proceedings of the Royal Society, London 29:365–367

    Article  Google Scholar 

  • George, A. and Mathai, A.M. (1975): A Generalized Distribution for Inter-Live Birth Interval. Sankhyā 37B:332–342

    MathSciNet  Google Scholar 

  • Heckman, J.J. and Singer, B. (1982): Population Hetzerogeneity in Demographic Models, pages 567 to 595, in Multidimensional Mathematical Demography, edited by K.C. Land and A. Rogers. Academic Press, New York and London

    Google Scholar 

  • Hewitt, E. and Savage, L.J. (1956): Symmetric Measures on Cortesian Products. Transactions of the American Mathematical Society 80:470–501

    Article  MathSciNet  Google Scholar 

  • Hobcraft, J., Menken, J. and Preston, S. (1982): Age, Period, and Cohort Effects in Demography — A Review. Population Index 48:4–43

    Article  Google Scholar 

  • Hobcraft, J. and Rodriguez, G. (1980): Methodological Issues in Life Table Analysis of Birth Histories. Seminar on The Analysis of Maternity Histories, London School of Hygiene and Tropical Medicine

    Google Scholar 

  • Hoem, J.M., Madsen, D., Nielsen, J.L, Ohlsen, E.M., Hansen, H.O. and Rennermalm, B. (1981): Experiments in Modelling Recent Danish Fertility Curves. Demography 18:231–244

    Article  Google Scholar 

  • Kennedy, W.J. and Gentle, J.E. (1980): Statistical Computing. Marcel Dekker, Inc., New York and Basel

    MATH  Google Scholar 

  • Keyfitz, N. (1968): Introduction to the Mathematics of Population. Addison-Wesley, Reading, Mass.

    Google Scholar 

  • Keyfitz, N. and Flieger, W. (1968): World Population. The University of Chicago Press, Chicago, III.

    Google Scholar 

  • Lee, C.F. and Lin, K.H. (1976): Parity Patterns of Birth Interval Distributions. Demography 13:45–64

    Article  Google Scholar 

  • Leridon, H. (1977): Human Fertility — The Basic Components. The University of Chicago Press, Chicago and London

    Google Scholar 

  • Littman, G.S. and Mode, C.J. (1977): A Non-Markovian Model for the Taichung Medical IUD Experiment. Mathematical Biosciences 34:279–302

    Article  MATH  Google Scholar 

  • Lotka, A.J. (1939): A Contribution to the Theory of Self-Renewing Aggregates With Special Reference to Industrial Replacement. Ann. Math. Stat. 10:1–25

    Article  MATH  Google Scholar 

  • Marquardt, D.W. (1963): An Algorithm for Least Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics 11:431–441

    Article  MATH  MathSciNet  Google Scholar 

  • McAlister, D. (1879): The Law of the Geometric Mean. Proceedings of the Royal Society, London. 29:367–375

    Article  Google Scholar 

  • McClelland, G.H. (1979): Determining the Impact of Sex Preferences on Fertility: A Consideration of Parity Progression Ratio, Dominance, and Stopping Rule Measures. Demography 16:377–388

    Article  Google Scholar 

  • Mode, C.J. (1967): A Renewal Density Theorem in the Multi-Dimensional Case. Journal of Applied Probability 4:62–76

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1975): Perspectives in Stochastic Models of Human Reproduction — A Review and Analysis. Theoretical Population Biology 8:247—291

    Article  MathSciNet  Google Scholar 

  • Mood, A.M. and Graybill, F.A. (1963): Introduction to the Theory of Statistics. McGraw-Hill, New York

    Google Scholar 

  • Pathak, K.B. (1971): A Stochastic Model for the Study of Open Birth Interval — A Cohort Approach. Sankhyā 33B:305–314

    Google Scholar 

  • Pickens, G.T. (1980): A Stochastic Model of Natural Fertility ā Theory and Analysis of Some Historical Population Data. Mathematical Biosciences 48:129–151

    Article  MATH  Google Scholar 

  • Poole, W.K. (1973): Fertility Measures Based on Birth Interval Data. Theoretical Population Biology 4:357–387

    Article  MathSciNet  Google Scholar 

  • Potter, R.G. (1963): Birth Intervals — Structure and Change. Population Studies 17:155–166

    Google Scholar 

  • Pretorius, S.J. (1930): Skew Bivariate Frequency Surfaces Examined in the Light of Numerical Illustrations. Biometrika 22:109–223

    MATH  Google Scholar 

  • Pullum, T.W. (1979): Adjusting Stated Fertility Preferences for the Effect of Actual Family Size With Application to World Fertility Survey Data. Paper presented at Annual Meeting of PAA, Philadelphia, Pa.

    Google Scholar 

  • Révész, P. (1968): The Laws of Large Numbers. Academic Press, New York and London

    MATH  Google Scholar 

  • Ross, J.A. and Madhavan, S. (1981): A Gompertz Model for Birth Interval Analysis. Population Studies 35:439–454

    Google Scholar 

  • Ruzicka, L.T. (1976): Age at Marriage and Timing of the First Birth. Population Studies 30:527–538

    Google Scholar 

  • Sheps, M.C. (1963): Effects on Family Size and Sex Ratio of Preferences Regarding Sex of Children. Population Studies 17:66–72

    Google Scholar 

  • Sheps, M.C. (1965): An Analysis of Reproductive Patterns in an American Isolate. Population Studies 19:65–80

    Google Scholar 

  • Sheps, M.C. and Menken, J.A. (1973): Mathematical Models of Conception and Birth. The University of Chicago Press

    Google Scholar 

  • Singh, S.N. (1964): On the Time of First Birth. Sankhyā 26B:95–102

    Google Scholar 

  • Singh, S.N. (1968): A Chance Mechanism of Variation in the Number of Births per Couple. Journal of American Statistical Association 63:209–213

    Article  Google Scholar 

  • Singh, S.N., Bhattacharya, B.N. and Yadava, R.C. (1974): A Parity Dependent Model for Number of Births and Its Applications. Sankhyā 36B:93–102

    Google Scholar 

  • Singh, S.N., Bhattacharya, B.N. and Yadava, R.C. (1979): An Adjustment of a Selection Bias in Post-Partum Amenorrhea From Follow-Up Studies. Journal of American Statistical Association 74:916–920

    Article  Google Scholar 

  • Singh, S.N., Chakrabarty, K.C. and Barman, D. (1981): On Estimating the Risk of Conception From Observations on First Contraceptive Delays. Journal of Theoretical Biology 90:1–7

    Article  Google Scholar 

  • Singh, S.N., Chakrabarty, K.C. and Singh, V.K. (1976): A Modification of a Continuous Time Model for First Conception. Demography 13:37–44

    Article  Google Scholar 

  • Suchindran, C.M. and Lachanbruch, P.A. (1974): Estimates of Parameters in Probability Model for First Live Birth Interval. Journal American Statistical Association 69:507–513

    Article  Google Scholar 

  • Suchindran, C.M. and Linger, J.W. (1977): On Comparison of Birth Interval Distributions. Journal of Biosocial Science 9:25–31

    Article  Google Scholar 

  • Svinivasan, K. (1968): A Set of Analytical Models for the Study of Open Birth Intervals. Demography 5:34–44

    Google Scholar 

  • Tuan, C.H. (1958): Reproductive Histories of Chinese Women in Rural Taiwan. Population Studies 12:40–50

    Google Scholar 

  • Venkatacharya, K. (1972): Some Problems in the Use of Open Birth Intervals as Indicators of Fertility Change. Population Studies 26:495–505

    Google Scholar 

  • Watkins, S.C. and McCarthy, J. (1980): The Female Life Cycle in a Belgian Commune — La Hulpe, 1847–1866. Journal of Family History 5:167–179

    Article  Google Scholar 

  • Wilks, S.S. (1962): Mathematical Statistics. John Wiley and Sons, New York

    MATH  Google Scholar 

  • Wolfers, D. (1968): Determinants of Birth Intervals and Their Means. Population Studies 22:253–262

    Google Scholar 

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  1. Department of Mathematics and Computer Science College of Science, Drexel University, Philadelphia, PA, 19104, USA

    Charles J. Mode

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© 1985 Springer-Verlag Berlin Heidelberg

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Mode, C.J. (1985). Models of Maternity Histories and Age-Specific Birth Rates. In: Stochastic Processes in Demography and Their Computer Implementation. Biomathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82322-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-82322-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82324-4

  • Online ISBN: 978-3-642-82322-0

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