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Population Projection Methodology Based on Stochastic Population Processes

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Stochastic Processes in Demography and Their Computer Implementation

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

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Abstract

Models of maternity histories in female birth cohorts, although interesting in their own right, are only one facet of the dynamics of human populations. In order to gain insights into the implication of these models from the standpoint of the evolutionary development of human populations, they need to be linked, primarily through cohort fertility density functions, to a methodology for making population projections. The primary purpose of this chapter is to provide such a linkage to a population projection methodology based on a class of stochastic processes in discrete time with either time homogeneous or time inhomogeneous laws of evolution.

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References

  • Asmussen, S. and Hering, H. (1983): Branching Processes. Birkhäuser, Boston, Basel, Stuttgart

    MATH  Google Scholar 

  • Athreya, K.B. and Ney, P. (1972): Branching Processes. Springer-Verlag, Berlin, Heidelberg, New York

    MATH  Google Scholar 

  • Baraabba, V.P., Mason, R.O. and Mitroff, I.I. (1983): Federal Statistics in a Complex Environment. The American Statistician 37:203–212

    Article  Google Scholar 

  • Chandrasekaran, C. and Hermalin, A.I. (Editors) (1975): Measuring the Effect of Family Planning Programs on Fertility. Ordina Editions, 4830 Dolhain, Belgium

    Google Scholar 

  • Coale, A.J. and Demeny, P. (1966): Regional Model Life Tables and Stable Populations. Princeton University Press, Princeton, New Jersey

    Google Scholar 

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

    Google Scholar 

  • Coale, A.J. (1983): Recent Trends in Fertility in Less Developed Countries. Science 221:828–832

    Article  Google Scholar 

  • Cohen, J.E. (1976): Ergodicity of Age-Structure in Populations with Markovian Vital Rates I: Countable States. J. Amer. Statist. Assoc. 71:335–339

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen, J.E. (1977a): Ergodicity of Age-Structure in Populations with Markovian Vital Rates II: General States. Advances in Appl. Probability 9:18–37

    Article  MATH  Google Scholar 

  • Cohen, J.E. (1977b): Ergodicity of Age-Structure in Populations with Markovian Vital Rates III: An Illustration. Advances in Appl. Probability 9:462–475

    Article  MATH  Google Scholar 

  • Crump, K.S. and Mode, C.J. (1968): A General Age-Dependent Branching Process I. Jour. Math. Anal. Appl. 24:494–508

    Article  MATH  MathSciNet  Google Scholar 

  • Crump. K.S. and Mode C.J. (1969): A General Age-Dependent Branching Process II. J. Math. Anal. Appl. 25:8–17

    Article  MATH  MathSciNet  Google Scholar 

  • Feller, W. (1968): An Introduction to Probability Theory and Its Applications. Vol.I, 3rd ed., John Wiley and Sons, New York

    MATH  Google Scholar 

  • Fisher, R.A. (1958): The Genetical Theory of Natural Selection. Dover, New York

    Google Scholar 

  • Harris, T.E. (1963): The Theory of Branching Processes. Springer-Verlag, Berlin Göttingen, Heidelberg

    MATH  Google Scholar 

  • Jagers, P. (1969): A General Stochastic Model for Population Development. Skandinavisk Aktuarietidskift 84–103

    Google Scholar 

  • Jagers, P. (1975): Branching Processes with Biological Applications. John Wiley and Sons, London, New York, Sydney, Toronto

    MATH  Google Scholar 

  • Jagers, P. (1982): How Probable Is It To Be Birst Born? — And Other Branching Process Applications to Kinship Problems. Mathematical Biosciences 59:1–15

    Article  MATH  MathSciNet  Google Scholar 

  • Joffe, A. and Ney, P. (Editors) (1978): Branching Processes. Marcel Dekker, New York

    MATH  Google Scholar 

  • Joffe, A. and Waugh, W.A.O’N. (1982): Exact Distributions of Kin Numbers in a Galton-Watson Process. Jour. Appl. Prob. 19:767–775

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Keyfitz, N. (1971): On the Momentum of Population Growth. Demography 8:71–80

    Article  Google Scholar 

  • Keyfitz, N. (1981): The Limits of Population Forecasting. Population Development and Review 7:579–593

    Article  Google Scholar 

  • Keyfitz, N. (1982): Can Knowledge Improve Forecasts? Population Development and Review 8:729–751

    Article  Google Scholar 

  • Krishnamoorthy, S., Potter, R.G. and Pickard, D.K. (1981): Population Momentum — Its Relation to the Moments of Replacement Level Fertility. Mathematical Biosciences 53:41–51

    Article  MATH  Google Scholar 

  • Leslie, PH. (1945): On the Use of Matrices in Certain Population Mathematics. Biometrika 33:183–212

    Article  MATH  MathSciNet  Google Scholar 

  • Leslie, P.H. (1948): Some Further Notes on the Use of Matrices in Population Mathematics. Biometrika 35:213–245

    MATH  MathSciNet  Google Scholar 

  • Lotka, A.J. (1956): Elements of Mathematical Biology. Dover, New York, N.Y.

    MATH  Google Scholar 

  • Mitra, S. (1976): Influence of Instantaneous Fertility Decline to Replacement Level on Population Growth. Demography 13:513–520

    Article  Google Scholar 

  • Mode, C.J. (1971): Multitype Branching Processes — Theory and Applications. American Elsevier, New York

    MATH  Google Scholar 

  • Mode, C.J. (1972): A Bisexual Multi-Type Branching Process and Applications in Population Genetics. The Bulletin of Mathematical Biophysics 34:13–31

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1974a): Discrete Time Age-Dependent Branching Processes in Relation to Stable Population Theory in Demography. Mathematical Biosciences 19:73–100

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1974b): Applications of Terminating Nonhomogeneous Renewal Processes in Family Planning Evaluation. Mathematical Biosciences 22:293–311

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1974c): A Discrete Time Stochastic Growth Process for Human Populations Accommodating Marriages. Mathematical Biosciences 9:201–219

    Article  Google Scholar 

  • Mode, C.J. (1974d): On the Evaluation of a Determinant Arising in a Bisexual Stochastic Growth Process. Journal of Mathematical Analysis and Its Applications 46:190–211

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1976): Age-Dependent Branching Processes and Sampling Frameworks for Mortality and Marital Variables in Non-Stable Populations. Mathematical Biosciences 30:47–67

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. (1977): A Population Projection Component of a Computer System-Population Policies and Birth Targets. Mathematical Biosciences 36:87–107

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. and Busby, R.C (1981): Algorithms for a Projection Model of Demographic Indicators Based on Generalized Branching Processes. Mathematical Biosciences 57:83–107

    Article  MATH  MathSciNet  Google Scholar 

  • Mode, C.J. and Littman, G.S. (1974): Applications of Computerized Stochastic Models of Human Reproduction and Population Growth in Family Planning Evaluation. Mathematical Biosciences 20:267–292

    Article  MATH  Google Scholar 

  • Pickens, G.T., Busby, R.C and Mode, C.J. (1983): Computerization of a Population Projection Model Based on Generalized Branching Processes — A Connection with the Leslie Matrix. Mathematical Biosciences 64:91–97

    Article  MATH  Google Scholar 

  • Pollard, J.H. (1966): On the Use of the Direct Matrix Product in Analysing Certain Stochastic Models. Biometrika 53:397–415

    MATH  MathSciNet  Google Scholar 

  • Pollard, J.H. (1973): Mathematical Models for the Growth of Human Populations. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Pullum, T.W. (1982): The Eventual Frequencies of Kin in a Stable Population. Demography 19:549–565

    Article  Google Scholar 

  • Ross, J.A. (1975): Acceptor Targets. In Measuring the Effect of Family Planning Programs on Fertility, ed. by C. Chandrasekaran and A.I. Hermilin. Ordina Editions, 4830 Dolhain, Belgium

    Google Scholar 

  • Sevast’yanov, B.A. (1974): Verzweigungs-Prozesse. Akademie-Verlag, Berlin.

    Google Scholar 

  • Smith, D. and Keyfitz, N. (1977): Mathematical Demography — Selected Papers. Springer-Verlag, Berlin, Heidelberg, New York

    MATH  Google Scholar 

  • Sykes, Z.M. (1969): On Discrete Stable Population Theory. Biometrics 25:285–293

    Article  Google Scholar 

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Authors and Affiliations

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

    Charles J. Mode

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  1. Charles J. Mode
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© 1985 Springer-Verlag Berlin Heidelberg

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Mode, C.J. (1985). Population Projection Methodology Based on Stochastic Population Processes. 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_7

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  • DOI: https://doi.org/10.1007/978-3-642-82322-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82324-4

  • Online ISBN: 978-3-642-82322-0

  • eBook Packages: Springer Book Archive

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