Stochastic Processes in Demography and Their Computer Implementation

Stochastic Processes in Demography and Their Computer Implementation

by C.J. Mode

Paperback(Softcover reprint of the original 1st ed. 1985)

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Product Details

ISBN-13: 9783642823244
Publisher: Springer Berlin Heidelberg
Publication date: 12/15/2011
Series: Biomathematics , #14
Edition description: Softcover reprint of the original 1st ed. 1985
Pages: 390
Product dimensions: 6.69(w) x 9.61(h) x 0.03(d)

Table of Contents

1. Fecundability.- 1.1 Introduction.- 1.2 A Model of Constant Fecundability — The Geometric Distribution.- 1.3 Applying the Geometric Distribution to Data.- 1.4 A Model of Heterogeneous Fecundability.- 1.5 Some Properties of the Beta-Geometric Distribution.- 1.6 Applying the Beta-Geometric Distribution to Data.- 1.7 An Investigation of Selectivity.- 1.8 Fecundability as a Function of Coital Pattern.- 1.9 A Distribution on the Set of Coital Patterns.- 1.10 Some Implications of Markov Chain Model of Coital Patterns.- 1.11 Computer Implementation and Numerical Examples.- 1.12 Conclusions and Further Research Directions.- Problems and Miscellaneous Complements.- References.- 2. Human Survivorship.- 2.1 Introduction.- 2.2 Mortality in a Cohort.- 2.3 Simple Parametric Examples of the Force of Mortality.- Examples: 2.3.1 The Exponential Distribution 37. — 2.3.2 The Weibull Distribution 38. — 2.3.3 The Gompertz Distribution.- 2.4 Period Mortality — A Simple Algorithm.- 2.5 Transforming Central Death Rates into Probabilities and Expectations.- 2.6 Evolutionary Changes in Expectation of Life.- 2.7 An Evolutionary Process Governing Survivorship.- 2.8 Historical Attempts at Modeling Survivorship.- 2.9 Modeling a Force of Mortality for the Whole of Life.- 2.10 Computer Experiments in Fitting Survivorship Models to Swedish Historical Data.- 2.11 Heterogeneity in Survivorship.- 2.12 Further Reading.- Problems and Miscellaneous Complements.- References.- 3. Theories of Competing Risks and Multiple Decrement Life Tables.- 3.1 Introduction.- 3.2 Mortality in a Cohort with Competing Risks of Death.- 3.3 Models of Competing Risks Based on Latent Life Spans.- 3.4 Simple Parametric Models of Competing Risks.- Examples: 3.4.1 Constant Forces of Mortality 81. — 3.4.2 A Survival Function on R3+.- 3.5 Equivalent Models of Competing Risks.- 3.6 Eliminating Causes of Death and Nonidentifiability.- Examples: 3.6.1 A Case where the Functions S (3, x) and S0 (3, x) Differ 86. — 3.6.2 A Graphical Example Comparing the Survival Functions S (x), S (3, x), and S0 (3, x).- 3.7 Estimating a Multiple Decrement Life Table from Period Data.- 3.8 Estimating Single Decrement Life Tables from Multiple Decrement Life Tables.- 3.9 Evolutionary Changes in the Structure of Causes of Death.- 3.10 Graphs of Multiple Decrement Life Tables — A Study of Proportional Forces of Mortality.- 3.11 Graphs of Single Decrement Life Tables Associated with Multiple Decrement Tables.- 3.12 Graphs of Latent Survival Functions and Forces of Mortality.- 3.13 An Evolutionary Model of Competing Risks.- Problems and Miscellaneous Complements.- References.- 4. Models of Maternity Histories and Age-Specific Birth Rates.- 4.1 Introduction.- 4.2 A Potential Birth Process.- 4.3 Cohort Net and Gross Maternity Functions.- 4.4 Parity Progression Ratios.- 4.5 Parametric Distributions of Waiting Times Among Live Births.- Examples: 4.5.1 Applications of the Exponential Distribution 122. — 4.5.2 A Simplified Model Based on the Exponential Distribution 123. — 4.5.3 A Double Exponential Distribution 124. — 4.5.4 Distributions Based on Risk Functions.- 4.6 Parametric Forms of the Distribution of Age at First Marriage in a Cohort.- 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 130. — 4.6.4 On the Joint Distribution of the Ages of Brides and Grooms — The Bivariate Lognormal.- 4.7 Heterogeneity in Waiting Times Among Live Births.- 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.- 4.8 An Age-Dependent Potential Birth Process.- Example: 4.8.1 Maternity Histories in a Nineteenth Century Belgian Commune — La Hulpe.- 4.9 An Evolutionary Potential Birth Process.- 4.10 The Evolution of Period Fertility in Sweden — 1780 to 1975.- 4.11 Further Reading.- Problems and Miscellaneous Complements.- References.- 5. A Computer Software Design Implementing Models of Maternity Histories.- 5.1 Introduction.- 5.2 Semi-Markov Processes in Discrete Time with Stationary Transition Probabilities.- 5.3 A Decomposition of Birth Intervals.- 5.4 On Choosing Component Functions of the Model.- 5.5 An Overview of MATHIST — A Computer Simulation System.- 5.6 Applications of MATHIST — Two Simulation Runs in Class One.- 5.7 A Factorial Experiment Based on Class Two Runs in MATHIST.- 5.7.1 An Overview of Computer Input.- 5.7.2 Phenomenological and Population Policy Implications of Simulated Cohort Total Fertility Rates and Their Variances.- Phenomenological Implications.- Implications for Population Policy.- 5.7.3 Comparisons of Simulated Cohort and Period Age — Specific Fertility Rates.- Comparisons of Total Fertility Rates.- Comparisons of Birth Rates for the Age Group [15, 20).- Comparisons of Age Groups with Maximum Birth Rates.- On the Plausibility of the Mathematical Assumptions Underlying MATHIST.- 5.7.4 Computer Generated Graphs of Selected Output from MATHIST.- 5.8 A Stochastic Model of Anovulatory Sterile Periods Following Live Births.- Example: 5.8.1 Numerical Examples Based on a Parametric Model.- 5.9 A Semi-Markovian Model for Waiting Times to Conception Under Contraception.- 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.- 5.10 Notes on Cohort and Period Projections of Fertility.- 5.11 Further Reading.- Problems and Miscellaneous Complements.- References.- 6. Age-Dependent Models of Maternity Histories Based on Data Analyses.- 6.1 Introduction.- 6.2 Age-Dependent Semi-Markov Processes in Discrete Time with Stationary Transition Probabilities.- 6.3 An Age-Dependent Semi-Markovian Model of Maternity Histories.- 6.4 On Choosing Computer Input for an Age-Dependent Model of Maternity Histories.- 6.5 Estimates of Fecundability Functions Based on Null Segments and Other Computer Input.- 6.6 Numerical Specifications of Four Computer Runs with Inputs Based on Survey Data.- 6.7 Computer Output Based on Survey Data.- 6.8 Further Assessment of the Quality of Calculations in Sect. 6.7 and Conclusions.- 6.9 A Non-Markovian Model for the Taichung Medical IUD Experiment.- 6.10 Estimates of Transition Functions Associated with First IUD Segment in Taichung Model.- 6.11 Validation of Taichung Model.- 6.12 State and Fertility Profiles for Taichung Limiters.- 6.13 Implications of the Taichung Experiment for Evaluating Family Planning Programs.- 6.14 On Measuring the Fertility Impact of Family Planning Programs.- 6.15 Conclusions and Further Reading.- Problems and Miscellaneous Complements.- References.- 7. Population Projection Methodology Based on Stochastic Population Processes.- 7.1 Introduction.- 7.2 Basic Functions Underlying a Branching Process.- 7.3 Basic Random Functions and Their Means.- 7.4 Explicit Formulas for Mean Functions.- 7.5 Leslie Matrix Type Recursive Formulas for Mean Functions.- 7.6 A Brief Review of Literature.- 7.7 Stochastic Variability in Population Structure as a Gaussian Process.- 7.8 A Representation of Population Structure Based on Birth Cohorts.- 7.9 Covariance Functions for the Birth Process and Live Individuals.- 7.10 Product Moments of the Actual and Potential Birth Processes.- 7.11 Product Moment Functions as Solutions of Renewal Equations.- 7.12 Asymptotic Formulas for Mean and Covariance Functions in the Time Homogeneous Case.- 7.13 Period Demographic Indicators in Populations with Time Inhomogeneous Laws of Evolution.- 7.14 Asymptotic Formulas for Period Demographic Indicators in the Time Homogeneous Case.- 7.15 A Female Dominant Two-Sex Population Process.- 7.16 An Overview of a Computer Software Design Implementing Population Projection Systems.- 7.17 Four Computer Runs in the Time Homogeneous Case — A Study of Population Momentum.- 7.17.1 Guidelines for Interpreting Graphs of Period Mean Total Population.- 7.17.2 Guidelines for Interpreting Graphs of Period Rates of Population Growth, Crude Birth Rates, and Crude Death Rates.- 7.17.3 Guidelines for Interpreting Graphs of Distances of Period Age Distributions from Their Asymptotic Stable Forms.- 7.17.4 Implications for Population Policy.- 7.18 A Study of Changing Mortality and Constant Fertility in the Time Inhomogeneous Case.- 7.18.1 Guidelines for Interpreting Mean Total Population and Mean Total Births and Deaths.- 7.18.2 Guidelines for Interpreting Period Crude Birth and Death Rates and Rates of Population Growth.- 7.18.3 Guidelines for Interpreting Period Age Densities in the Time Inhomogeneous Run.- 7.19 Further Reading.- Problems and Miscellaneous Complements.- References.- Author Index.

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