Stochastic processes in demography and their computer implementation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1985
|
| Schriftenreihe: | Biomathematics
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 389 S. graph. Darst. |
| ISBN: | 3540136223 0387136223 |
Internformat
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| 245 | 1 | 0 | |a Stochastic processes in demography and their computer implementation |c C. J. Mode |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1985 | |
| 300 | |a XVII, 389 S. |b graph. Darst. | ||
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| 650 | 4 | |a Population - Modèles mathématiques | |
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| 650 | 4 | |a Demography | |
| 650 | 4 | |a Models, Theoretical | |
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Datensatz im Suchindex
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Contents
Chapter 1. Fecundability 1
1.1 Introduction 1
1.2 A Model of Constant Fecundability The Geometric Distribution . 1
1.3 Applying the Geometric Distribution to Data 3
1.4 A Model of Heterogeneous Fecundability 6
1.5 Some Properties of the Beta Geometric Distribution 8
1.6 Applying the Beta Geometric Distribution to Data 10
1.7 An Investigation of Selectivity 13
1.8 Fecundability as a Function of Coital Pattern 14
1.9 A Distribution on the Set of Coital Patterns 17
1.10 Some Implications of Markov Chain Model of Coital Patterns . 20
1.11 Computer Implementation and Numerical Examples 22
1.12 Conclusions and Further Research Directions 26
Problems and Miscellaneous Complements 28
References 33
Chapter 2. Human Survivorship 35
2.1 Introduction 35
2.2 Mortality in a Cohort 36
2.3 Simple Parametric Examples of the Force of Mortality 37
Examples: 2.3.1 The Exponential Distribution 37. 2.3.2 The Weibull Distribution 38.
2.3.3 The Gompertz Distribution 38
2.4 Period Mortality A Simple Algorithm 39
2.5 Transforming Central Death Rates into Probabilities
and Expectations 40
2.6 Evolutionary Changes in Expectation of Life 43
2.7 An Evolutionary Process Governing Survivorship 47
2.8 Historical Attempts at Modeling Survivorship 52
2.9 Modeling a Force of Mortality for the Whole of Life 55
2.10 Computer Experiments in Fitting Survivorship Models to Swedish
Historical Data 59
2.11 Heterogeneity in Survivorship 65
XIV Contents
2.12 Further Reading 68
Problems and Miscellaneous Complements 69
References 74
Chapter 3. Theories of Competing Risks and Multiple Decrement Life
Tables 76
3.1 Introduction 76
3.2 Mortality in a Cohort with Competing Risks of Death 77
3.3 Models of Competing Risks Based on Latent Life Spans 79
3.4 Simple Parametric Models of Competing Risks 81
Examples: 3.4.1 Constant Forces of Mortality 81. 3.4.2 A Survival Function on R~£
82
3.5 Equivalent Models of Competing Risks 82
3.6 Eliminating Causes of Death and Nonidentifiability 84
Examples: 3.6.1 A Case where the Functions S(3,x) and S°(3, x) Differ 86. 3.6.2 A
Graphical Example Comparing the Survival Functions S(x), S(3, x), and S°(3, x) 86
3.7 Estimating a Multiple Decrement Life Table from Period Data . . 87
3.8 Estimating Single Decrement Life Tables from Multiple Decrement
Life Tables 90
3.9 Evolutionary Changes in the Structure of Causes of Death . 93
3.10 Graphs of Multiple Decrement Life Tables A Study of
Proportional Forces of Mortality 95
3.11 Graphs of Single Decrement Life Tables Associated with Multiple
Decrement Tables 99
3.12 Graphs of Latent Survival Functions and Forces of Mortality . . . 101
3.13 An Evolutionary Model of Competing Risks 104
Problems and Miscellaneous Complements 106
References Ill
Chapter 4. Models of Maternity Histories and Age Specific Birth Rates . 112
4.1 Introduction 112
4.2 A Potential Birth Process 113
4.3 Cohort Net and Gross Maternity Functions 116
4.4 Parity Progression Ratios 119
4.5 Parametric Distributions of Waiting Times Among Live Births . .121
Examples: 4.5.1 Applications of the Exponential Distribution 122. 4.5.2 A Sim¬
plified Model Based on the Exponential Distribution 123. 4.5.3 A Double Ex¬
ponential Distribution 124. 4.5.4 Distributions Based on Risk Functions 126
4.6 Parametric Forms of the Distribution of Age at First Marriage
in a Cohort 128
Examples: 4.6.1 A Model Based on a Double Exponential Risk Function 128. 4.6.2
A Model Based on the Lognormal Distribution 129. 4.6.3 Validation of Lognormal
Contents XV
130. 4.6.4 On the Joint Distribution of the Ages of Brides and Grooms The
Bivariate Lognormal 133
4.7 Heterogeneity in Waiting Times Among Live Births 136
Examples: 4.7.1 Gamma Mixtures of Gamma Distributions 137. 4.7.2 Variances,
Covariances, and Correlations of Waiting Times Among Live Births 140. 4.7.3
Conditional Distributions of the Random Variable A 141. 4.7.4 Distribution of
Waiting Times to n th Live Birth 142
4.8 An Age Dependent Potential Birth Process 144
Example: 4.8.1 Maternity Histories in a Nineteenth Century Belgian Commune La
Hulpe 149
4.9 An Evolutionary Potential Birth Process 153
4.10 The Evolution of Period Fertility in Sweden 1780 to 1975 . 159
4.11 Further Reading 163
Problems and Miscellaneous Complements 164
References 174
Chapter 5. A Computer Software Design Implementing Models of
Maternity Histories 177
5.1 Introduction 177
5.2 Semi Markov Processes in Discrete Time with Stationary Transition
Probabilities 177
5.3 A Decomposition of Birth Intervals 182
5.4 On Choosing Component Functions of the Model 187
5.5 An Overview of MATHIST A Computer Simulation System . . 194
5.6 Applications of MATHIST Two Simulation Runs in Class One . 201
5.7 A Factorial Experiment Based on Class Two Runs in MATHIST . . 204
5.7.1 An Overview of Computer Input 205
5.7.2 Phenomenological and Population Policy Implications of
Simulated Cohort Total Fertility Rates and Their Variances . 210
5.7.2.1 Phenomenological Implications 211
5.7.2.2 Implications for Population Policy 212
5.7.3 Comparisons of Simulated Cohort and Period Age Specific
Fertility Rates 213
5.7.3.1 Comparisons of Total Fertility Rates 214
5.7.3.2 Comparisons of Birth Rates for the Age Group
[15, 20) 214
5.7.3.3 Comparisons of Age Groups with Maximum Birth
Rates 215
5.7.3.4 On the Plausibility of the Mathematical Assumptions
Underlying MATHIST 216
5.7.4 Computer Generated Graphs of Selected Output from
MATHIST 219
5.8 A Stochastic Model of Anovulatory Sterile Periods Following Live
Births 221
XVI Contents
Example: 5.8.1 Numerical Examples Based on a Parametric Model 225
5.9 A Semi Markovian Model for Waiting Times to Conception Under
Contraception 228
Examples: 5.9.1 A One Step Transition Matrix of Density Functions for Spacers 231. .
5.9.2 A One Step Transition Matrix of Density Functions for Limiters 232
5.10 Notes on Cohort and Period Projections of Fertility 233
5.11 Further Reading 234
Problems and Miscellaneous Complements 235
References 241
Chapter 6. Age Dependent Models of Maternity Histories Based on Data
Analyses 243
6.1 Introduction 243
6.2 Age Dependent Semi Markov Processes in Discrete Time with
Stationary Transition Probabilities 244
6.3 An Age Dependent Semi Markovian Model of Maternity Histories . 248
6.4 On Choosing Computer Input for an Age Dependent Model of
Maternity Histories 256
6.5 Estimates of Fecundability Functions Based on Null Segments and
Other Computer Input 261
6.6 Numerical Specifications of Four Computer Runs with Inputs Based
on Survey Data 266
6.7 Computer Output Based on Survey Data 269
6.8 Further Assessment of the Quality of Calculations in Sect. 6.7 and
Conclusions 276
6.9 A Non Markovian Model for the Taichung Medical IUD
Experiment 280
6.10 Estimates of Transition Functions Associated with First IUD
Segment in Taichung Model 285
6.11 Validation of Taichung Model 288
6.12 State and Fertility Profiles for Taichung Limiters 293
6.13 Implications of the Taichung Experiment for Evaluating Family
Planning Programs 298
6.14 On Measuring the Fertility Impact of Family Planning Programs . 299
6.15 Conclusions and Further Reading 302
Problems and Miscellaneous Complements 304
References 307
Chapter 7. Population Projection Methodology Based on Stochastic
Population Processes 309
7.1 Introduction 309
7.2 Basic Functions Underlying a Branching Process 310
Contents XVII
7.3 Basic Random Functions and Their Means 312
7.4 Explicit Formulas for Mean Functions 315
7.5 Leslie Matrix Type Recursive Formulas for Mean Functions . . . 317
7.6 A Brief Review of Literature 320
7.7 Stochastic Variability in Population Structure as a Gaussian Process 322
7.8 A Representation of Population Structure Based on Birth Cohorts . 326
7.9 Covariance Functions for the Birth Process and Live Individuals . . 328
7.10 Product Moments of the Actual and Potential Birth Processes . . . 334
7.11 Product Moment Functions as Solutions of Renewal Equations . . 340
7.12 Asymptotic Formulas for Mean and Covariance Functions in the
Time Homogeneous Case 343
7.13 Period Demographic Indicators in Populations with Time
Inhomogeneous Laws of Evolution 347
7.14 Asymptotic Formulas for Period Demographic Indicators in the
Time Homogeneous Case 351
7.15 A Female Dominant Two Sex Population Process 354
7.16 An Overview of a Computer Software Design Implementing
Population Projection Systems 358
7.17 Four Computer Runs in the Time Homogeneous Case A Study of
Population Momentum 363
7.17.1 Guidelines for Interpreting Graphs of Period Mean Total
Population 367
7.17.2 Guidelines for Interpreting Graphs of Period Rates of
Population Growth, Crude Birth Rates, and Crude Death
Rates 367
7.17.3 Guidelines for Interpreting Graphs of Distances of Period
Age Distributions from Their Asymptotic Stable Forms . . . 368
7.17.4 Implications for Population Policy 371
7.18 A Study of Changing Mortality and Constant Fertility in the Time
Inhomogeneous Case 371
7.18.1 Guidelines for Interpreting Mean Total Population and
Mean Total Births and Deaths 373
7.18.2 Guidelines for Interpreting Period Crude Birth and Death
Rates and Rates of Population Growth 375
7.18.3 Guidelines for Interpreting Period Age Densities in the
Time Inhomogeneous Run 376
7.19 Further Reading 376
Problems and Miscellaneous Complements 377
References 383
Author Index 385
Subject Index 387 |
| any_adam_object | 1 |
| author | Mode, Charles J. 1927- |
| author_GND | (DE-588)1022188879 |
| author_facet | Mode, Charles J. 1927- |
| author_role | aut |
| author_sort | Mode, Charles J. 1927- |
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| building | Verbundindex |
| bvnumber | BV000263683 |
| callnumber-first | H - Social Science |
| callnumber-label | HB849 |
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| callnumber-search | HB849.51 |
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| callnumber-subject | HB - Economic Theory and Demography |
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| dewey-full | 304.6/028/54 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 304 - Factors affecting social behavior |
| dewey-raw | 304.6/028/54 |
| dewey-search | 304.6/028/54 |
| dewey-sort | 3304.6 228 254 |
| dewey-tens | 300 - Social sciences |
| discipline | Biologie Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV000263683 |
| illustrated | Illustrated |
| indexdate | 2025-01-28T11:10:18Z |
| institution | BVB |
| isbn | 3540136223 0387136223 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000160174 |
| oclc_num | 720813278 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-473 DE-BY-UBG DE-703 DE-739 DE-945 DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-473 DE-BY-UBG DE-703 DE-739 DE-945 DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XVII, 389 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Biomathematics |
| series2 | Biomathematics |
| spelling | Mode, Charles J. 1927- Verfasser (DE-588)1022188879 aut Stochastic processes in demography and their computer implementation C. J. Mode Berlin [u.a.] Springer 1985 XVII, 389 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Biomathematics 14 Population - Informatique Population - Modèles mathématiques Datenverarbeitung Mathematisches Modell Demography Models, Theoretical Population Data processing Population Mathematical models Bevölkerungsentwicklung (DE-588)4006292-2 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Computerunterstütztes Verfahren (DE-588)4139030-1 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Demographie (DE-588)4011412-0 gnd rswk-swf Bevölkerungsentwicklung (DE-588)4006292-2 s Mathematisches Modell (DE-588)4114528-8 s Computersimulation (DE-588)4148259-1 s DE-604 Datenverarbeitung (DE-588)4011152-0 s Demographie (DE-588)4011412-0 s Stochastischer Prozess (DE-588)4057630-9 s Stochastisches Modell (DE-588)4057633-4 s Computerunterstütztes Verfahren (DE-588)4139030-1 s Biomathematics 14 (DE-604)BV000894631 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000160174&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mode, Charles J. 1927- Stochastic processes in demography and their computer implementation Biomathematics Population - Informatique Population - Modèles mathématiques Datenverarbeitung Mathematisches Modell Demography Models, Theoretical Population Data processing Population Mathematical models Bevölkerungsentwicklung (DE-588)4006292-2 gnd Stochastisches Modell (DE-588)4057633-4 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Demographie (DE-588)4011412-0 gnd |
| subject_GND | (DE-588)4006292-2 (DE-588)4057633-4 (DE-588)4139030-1 (DE-588)4011152-0 (DE-588)4148259-1 (DE-588)4114528-8 (DE-588)4057630-9 (DE-588)4011412-0 |
| title | Stochastic processes in demography and their computer implementation |
| title_auth | Stochastic processes in demography and their computer implementation |
| title_exact_search | Stochastic processes in demography and their computer implementation |
| title_full | Stochastic processes in demography and their computer implementation C. J. Mode |
| title_fullStr | Stochastic processes in demography and their computer implementation C. J. Mode |
| title_full_unstemmed | Stochastic processes in demography and their computer implementation C. J. Mode |
| title_short | Stochastic processes in demography and their computer implementation |
| title_sort | stochastic processes in demography and their computer implementation |
| topic | Population - Informatique Population - Modèles mathématiques Datenverarbeitung Mathematisches Modell Demography Models, Theoretical Population Data processing Population Mathematical models Bevölkerungsentwicklung (DE-588)4006292-2 gnd Stochastisches Modell (DE-588)4057633-4 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Demographie (DE-588)4011412-0 gnd |
| topic_facet | Population - Informatique Population - Modèles mathématiques Datenverarbeitung Mathematisches Modell Demography Models, Theoretical Population Data processing Population Mathematical models Bevölkerungsentwicklung Stochastisches Modell Computerunterstütztes Verfahren Computersimulation Stochastischer Prozess Demographie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000160174&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000894631 |
| work_keys_str_mv | AT modecharlesj stochasticprocessesindemographyandtheircomputerimplementation |