Introduction to the mathematics of population with revisions
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass.
Addison-Wesley
1977
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| Ausgabe: | Rev. print. |
| Schriftenreihe: | Addison-Wesley series in behavioral science: quantitative methods.
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Introduction to the mathematics of population |b with revisions |c Nathan Keyfitz |
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| 264 | 1 | |a Reading, Mass. |b Addison-Wesley |c 1977 | |
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Datensatz im Suchindex
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| adam_text | CONTENTS PART I THE LIFE TABLE Chapter 1 The Stationary Population Model 1.1 An Account of the Life Table.................................................................... 1.2 Inferring Probabilities from Rates........................................................ 19 1.3 Levels of Discourse..................................................................................... 24 3 PART II DISCRETE ANALYSIS FOR ONE SEX Chapter 2 The Basic Set of Recurrence Equations 2.1 Population Projection............................................................................... 27 2.2 Condensation of the Matrix.................................................................... 37 Chapter 3 3.1 3.2 3.3 3.4 Chapter 4 4.1 4.2 4.3 4.4 4.5 General Analysis of the Projection Matrix A Numerical Example for the 3X3 Matrix........................................41 Matrix Algebra of the Projection Process....................................................47 Iterative Calculation of Matrix Components........................................63 Interpretation of Results................................................................................ 69 Projection Matrix Changing Through Time Experiments on the Effects of Change in Birth and Death Rates ... 74 Analysis of Collections of Life Tables......................................................... 81 Extrapolation to Future Populations............................................................... 86 Adjustment of Data............................................................................................88 On Strong and Weak
Ergodicity.....................................................................89 PART III THE CONTINUOUS ANALYSIS Chapter 5 5.1 5.2 5.3 5.4 5.5 The Renewal Equation: General Solution Population Projection in the Continuous Case..............................................97 Solution by Elementary Calculus...................................................................100 Numerical Solution of the Characteristic Equation.................................108 Properties of the Laplace Transform .........................................................114 General Solution via the Laplace Transform............................................ 116 xi
ХІІ CONTENTS 5.6 The Succession of Generations.............................................................117 5.7 Point and Rectangular Distributions of the Net Maternity Function . 127 5.8 Formulation Through Generating Functions and Partial Fractions . . 130 Chapter 6 Parametrization of the Renewal Process 6.1 Graduating the Net Maternity Function................................................. 140 6.2 Graduation of the Net Maternity Function by the Normal Distribution (Lotka).............................................................................. 141 6.3 Graduation by the Incomplete Gamma Function (Wicksell) .... 147 6.4 Graduation by a Distribution that fits the Successive Generations (Hadwiger)............................................................................................... 149 6.5 Fit of the Several Graduations of the Net Maternity Function . . . 155 Chapter 7 7.1 7.2 7.3 7.4 Chapter 8 Interrelationships of Demographic Variables in Stable Populations Relations in any Closed Population.......................................................170 Relations Under Stability........................................................................ 174 An Application of Stable Theory............................................................ 184 Some Effects of Fertility and Mortality Change on Age Distribution . 185 Reconciliation of Matrix and Integral Equation 8.1 A Higher-Order Difference Equation................................................. 195 8.2 Matrix and Integral Equation.................................................................. 200
8.3 Summary of Solutions..............................................................................206 Chapter 9 Population Time Series 9.1 Births Corresponding to Given Total Numbers......................................210 9.2 Graduation by a Curve in which the Constants Enter Nonlinearly . . 214 9.3 The Near-Logistic Form of Births in a Population Growing Logistically............................................................................................... 218 9.4 The Population Explosion........................................ 219 PART IV NUMERICAL TECHNIQUES Chapter 10 10.1 10.2 10.3 10.4 10.5 Chapter 11 Interpolation and Graduation Straight-line Interpolation........................................................................... 223 Determinantal Expressions for Polynomial Interpolation....................... 224 Matrix Expressions for Polynomial Graduation................................... 232 Topics in Life Table Construction..........................................................234 The Estimate of Interpolation Error..........................................................244 Finite Approximations 11.1 The Projection Matrix . 11.2 The Stable Age Distribution Obtained from the 4 Column of the ..................................................................... 246 Life Table........................................ .................................................... 259
CONTENTS XIII 11.3 Stable Populations Changed from one Finite Approximation to Another....................................................................... 262 11.4 The Constants Q of the Integral Equation................................................264 11.5 Summary and Numerical Computation on Four Formulations of the Renewal Process........................................................................................265 PART V MULTIPLE POPULATIONS IN INTERACTION Chapter 12 Qualitative Aspects of Interaction among Populations 12.1 The Linear Model............................................................................. 271 12.2 A Nonlinear Case..............................................................................................284 12.3 The General Nonlinear Model..................................................................... 287 Chapter 13 13.1 13.2 13.3 13.4 13.5 Chapter 14 The Problem of the Sexes and other uses of Simultaneous Differential Equations Inconsistency in Treating theSexes Separately............................................... 293 Dominance.....................................................................................................296 Simultaneous Treatment of Ages and Sexes............................................... 309 A Marriage Model.........................................................................................313 Parity and Birth Order by Age................................................................. 318 Interacting Populations Analyzed by Age 14.1 The Generalized
Matrix.................................................................................. 320 14.2 MuUiple Decrement................................................................. 333 14.3 The Integral Equation Modified to Allow for Birth Order .... 334 PART VI PROBABILITY MODELS Chapter 15 Sampling Variance of Demographic Characteristics 15.1 Life Table Functions ........................................................................................ 339 15.2 Fertility Functions..............................................................................................351 15.3 A Simplified Approach to Complex Samples.............................................. 353 Chapter 16 16.1 16.2 16.3 16.4 16.5 Chapter 17 17.1 17.2 17.3 17.4 Birth and Death Processes The Pure Birth Process and its Extensions.................................................... 360 A Birth, Death, and Immigration Model................................... 362 The Problem of the Sexes Treated Stochastically........................................ 368 A General Expression for Variances in Linear Population Models . . 375 Distribution of the Sex Ratio......................... v..........................................377 Population Distributions and Individual Behavior Stopping Rules................................................................................................... 379 Births as a Sequence in Time............................................................................384 Allowance for the Nonfecund Period of Pregnancy.................................. 390
Simulation......................................................................................................... 397
XIV CONTENTS Chapter 18 The Branching Process as a Population Model 18.1 Branching Theory .............................................................................................399 18.2 Abridged Method of Finding Probability of Extinction............................406 18.3 Effect of Change in Distribution onthe Probability of Extinction . . 410 Chapter 19 19.1 19.2 19.3 19.4 19.5 Chapter 20 20.1 20.2 20.3 20.4 20.5 An Overview of Mathematical Demography History and Boundaries............................................................................ 413 Future Population............................................................................................ 418 Comparison and Explanation..................................................................... 421 Beyond the Human One-Sex Model . 422 Spatial Aspects..................................................................................................423 Problems in the Mathematics of Population Populations that are not Age-dependent................................................... 425 The Life Table................................................................................................. 429 Stable Populations.................................................... 437 Intrinsic Rates..................................................................................................440 Projection....................................................................................................... 442
Bibliography.............................................................................................................445 Symbols......................................................................................................................... 471 Table of ex to Seven Digits......................................................................................... 481 Index......................................................................................................................... 483
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| author | Keyfitz, Nathan 1913-2010 |
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| discipline | Biologie Soziologie Wirtschaftswissenschaften |
| edition | Rev. print. |
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| indexdate | 2025-02-03T16:12:11Z |
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| isbn | 0201036495 |
| language | English |
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| physical | XIV, 490 S. graph. Darst. |
| publishDate | 1977 |
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| publishDateSort | 1977 |
| publisher | Addison-Wesley |
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| series2 | Addison-Wesley series in behavioral science: quantitative methods. |
| spellingShingle | Keyfitz, Nathan 1913-2010 Introduction to the mathematics of population with revisions Mathematisches Modell (DE-588)4114528-8 gnd Populationsdynamik (DE-588)4046803-3 gnd Demographie (DE-588)4011412-0 gnd Statistik (DE-588)4056995-0 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4046803-3 (DE-588)4011412-0 (DE-588)4056995-0 (DE-588)4037944-9 (DE-588)4151278-9 |
| title | Introduction to the mathematics of population with revisions |
| title_auth | Introduction to the mathematics of population with revisions |
| title_exact_search | Introduction to the mathematics of population with revisions |
| title_full | Introduction to the mathematics of population with revisions Nathan Keyfitz |
| title_fullStr | Introduction to the mathematics of population with revisions Nathan Keyfitz |
| title_full_unstemmed | Introduction to the mathematics of population with revisions Nathan Keyfitz |
| title_short | Introduction to the mathematics of population |
| title_sort | introduction to the mathematics of population with revisions |
| title_sub | with revisions |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Populationsdynamik (DE-588)4046803-3 gnd Demographie (DE-588)4011412-0 gnd Statistik (DE-588)4056995-0 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematisches Modell Populationsdynamik Demographie Statistik Mathematik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001253579&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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