ABSTRACT Taylor’s law states that the variance of population density in a given set of areas is a power function of its mean. When the exponent is equal to 2, the distribution of population densities between areas remains unchanged; when it is less than 2, the distribution converges toward the uniform distribution; when it is greater than 2, the densities become increasingly different from each other

ABSTRACT Median ranked set sampling is a sampling procedure used to estimate the population mean when the variable of interest is difficult or costly to measure. Two estimators for the population mean based on the minimum and maximum values of the auxiliary variable are built upon a successive use of ranks, second raw moments, and the linearly transformed auxiliary variable. The biases and the mean

The Fisher information matrix related to an order statistic and its concomitant used to order a bivariate random sample are obtained in the case of the shape-parameter vector of an iterated Farlie–Gumbel–Morgenstern bivariate distribution. They contain information conveyed by singly or multiply censored bivariate samples drawn from an iterated Farlie–Gumbel–Morgenstern bivariate distribution. Fisher

In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between

Trichomoniasis is a sexually transmitted disease caused by an infection from the parasite Trichomonas vaginalis. A model of its transmission shows a backward bifurcation when the basic reproduction number R 0 is less than one. A stable disease-free equilibrium co-exists with a stable endemic equilibrium with the consequence that the disease may invade the population even when R 0 < 1 . The backward

Stratification of population is a probability sampling design used to increase the precision of estimation. An efficient exponential ratio estimator allows estimating the population mean in stratified random sampling using an auxiliary variable. Its expected bias, expected mean square error, and minimum mean square error are expressed. The conditions for which the estimator is more efficient are obtained

In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An explicit formula of the limit distribution

The ratio content error estimators recommended by the United Nations Statistics Division for censuses do not cover content errors resulting from erroneous enumerations and omissions; thus they underestimate content errors. The “complete content error estimator” covers all content errors and is unbiased. It applies to any category of population.

Improved chain-ratio estimators for the population mean based on two-phase sampling are proposed when the study variable and two auxiliary variables comprise non-response. Auxiliary information is available for the first variable and not available for the second variable. Their biases and mean square errors are estimated under large sample approximation. Their efficiencies are compared with Hansen

(2019). Methods and applications in spatial demography. Mathematical Population Studies: Vol. 26, Methods and Applications in Spatial Demography I, pp. 183-184.

(2019). In memoriam: Jennifer Buher Kane (1979–2019) Mathematical Population Studies: Vol. 26, Methods and Applications in Spatial Demography I, pp. 185-185.

"The cohort parity analysis (CPA) model of David et al. (1988) is studied formally as a three-state parity-progression table. The general solution is found in a form of convex combination of a finite set of solutions which are described explicitly. A parameterization is suggested for a broad subset of solutions which includes two extreme solutions studied in the original publication and maintains the

"We present the proportional multi-state life table method, that makes the inclusion of multiple diseases better manageable and allows for comorbidity implicitly, without the need to define additional states. We implement the method for heart disease and stroke [among Dutch males in 1988], and look at the effect of hypothetical but not unrealistic changes in incidence and survival on disease prevalence

"The multistate life table (MLT) has been widely used by demographers for the past twenty years. However, the pivotal Markov condition upon which the entire methodology rests is rarely satisfied in practice. We lessen reliance upon the assumption by computing transition probabilities for longer periods of time than was previously practical. An extended Kaplan-Meier estimator accomplishes this task

"Sixty-five has long been thought of as the point of entry into ¿old age'. We propose a number of life table criteria for answering the following questions: If 65 was considered appropriate four decades ago, what is the corresponding age today? If 65 was (implicitly) a male-oriented definition four decades ago, as we believe it was, what would have been the appropriate definition for women at that

"In this paper we consider a two-sex population model proposed by Hoppenstead. We do not assume any special form of the mating function. We address the problem of existence and uniqueness of continuous and classical solutions. We give sufficient conditions for continuous solutions to exist globally and we show that they have in fact a directional derivative in the direction of the characteristic lines

"The overriding goal of this paper has been to move the analysis of incomplete data in the direction of modeling and away from the predominantly algorithmic approach that is commonly used. The framework for the modeling approach, including the use of the log-linear model, was originally suggested by Willekens (1982). This paper builds on his work by: (1) providing a justification for the use of synthetic

"The paper presents probability models to recover information on migration flows from incomplete data. Models are used to predict migration and to combine data from different sources.... Two models are considered: the binomial (multinomial) model, which underlies the logit model and the logistic regression, and the Poisson model, which underlies the loglinear model, the log-rate model and the Poisson

"A set of log-rate models is proposed to transform Rogers and Wilson's accounting-based migration models into statistics-oriented migration models. This study demonstrates not only how log-rate models can be used to replicate results generated from Rogers-Wilson's cohort and multi-region mobility models, but also how log-rate models can be used to make statistical inferences and to derive more parsimonious

"In this paper, we apply model schedules to graduate data on the internal and external regional [U.S.] migration patterns of the foreign-born population for the 1950-1990 period.... To find estimates of the unrecorded migration flows in-between for four census-defined periods in our study (that is, for 1950-1955, 1960-1965, 1970-1975, and 1980-1985) we interpolate between the data of adjacent census

"Section 2 will first extend the method of mixed estimation to maximum likelihood estimation in general. Then, we will review generalized linear models with logistic and Poisson regressions as examples. In Section 3 we discuss different approaches for formulating the auxiliary information in practice. Section 4 first reviews the method of Coale and Kisker, provides empirical estimates for it, and then

"This paper develops a forward demographic rates-based multiregional population model on the basis of a set of multiregional population accounts. Forward emigration rates and immigration flows are adopted to describe the external migrations. The model is used to make consistent multiregional population projections of China at a provincial level.... Three sets of multiregional population projections

"This paper uses a two-level nested logit model to explain the inter-stratum (city, town and rural county) and interprovincial migration behaviors of the young adults (aged 17-29) in China during a three-year period (1985-87), based on the micro data of the 1987 National Population Survey. The migration propensity of each person is represented by a departure probability and a destination choice probability

"This paper develops a multi-dimensional model for projecting households and population. The model is constructed to ensure consistency between the demographic events occurring to males and females as well as to parents and children. The model permits projection of characteristics of households, their members, and population structure, using data that are usually available from conventional sources

"This paper aims to construct a demographic microsimulation model, which is easily applicable to gene transmission..., and to examine the distribution of completed parity as a fertility measure at a population level according to the schedule of individual life course....The simulation model was applied to the data of the Gidra-speaking people living in the lowlands of Papua New Guinea."

"Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two-child families increases

"Models of the interaction of population, the economy, and the environment often contain nonlinear functional relationships and variables that move at different speeds. These properties foster apparent unpredictabilities in system behaviour. Using a simple deterministic model of demographic, economic and environmental interactions we illustrate the usefulness of geometric singular perturbation theory

"This paper aims to investigate some models for population projection under a gradual change in fertility schedule, and to evaluate integrals therein for their actual values.... Some formulae for population projection have been derived under stability conditions. The proposed formulae are also illustrated with some numerical values of the parameters involved therein. The merits and shortcomings are

This study examines the transition of a population to stability following a shift to a new fixed set of vital rates. Specifically, the authors develop a simple discrete population model and use it to derive an explicit solution for the birth trajectory. "The new vital rates interact with the population's initial age composition and generate birth waves whose amplitude and attenuation depend on the

"Distinction made between household-persons and household-markers [the person who identifies the family or household as a unit] is formalized in the notion of nested populations. This leads to an extension of the Leslie model into a formulation of growth for both population and households. The extended model involves the matrix presentation of household composition where ratios of household-persons

"This paper argues that it is premature to decide whether simple forecasting models in demography are more (or less) accurate than complex models and whether causal models are more (or less) accurate than noncausal models. It is also too early to say under what conditions one type of model can outperform another. The paper also questions the wisdom of searching for a single best model or approach.

"More and more population forecasts are being produced with associated 95 percent confidence intervals. How confident are we of those confidence intervals? In this paper, we produce a simulated dataset in which we know both past and future population sizes, and the true 95 percent confidence intervals at various future dates. We use the past data to produce population forecasts and estimated 95 percent

"We have described a method for reducing the dimensionality of the forecasting problem by parsimoniously modeling the evolution over time of the age schedules of vital rates. This method steers a middle course between forecasting aggregates and forecasting individual age specific rates: we reduce the problem to forecasting a single parameter for fertility and another one for mortality. We have described

"This paper reviews the growing literature on population forecasting to examine a curious paradox: despite continuing refinements in the specification of models used to represent population dynamics, simple exponential growth models, it is claimed, continue to outperform such more complex models in forecasting exercises. Shrinking a large complex model in order to simplify it typically involves two

"An age-structured model of population dynamics with age-dominance is proposed and analyzed. Existence and uniqueness of solutions are established as well as the uniqueness and local asymptotic stability of steady-states. Conditions for convergence to or oscillation about the steady-state are specified in some cases." (SUMMARY IN FRE)

"We consider a Leslie-type model of a one-sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with

"Many ideas in the analysis of heterogeneous mortality are based on the relationship between individual and observed hazard rates. This connection is established with the help of conditional averaging procedure: The observed risk of death at age x is calculated among those who survive this age. The analogy of this result for bivariate survival model with correlated individual hazards is derived. In

"It is often observed that mortality projections are more pessimistic when disaggregated by cause of death. This article explores the generality and strength of this relationship under a variety of forecasting models. First, a simple measure of the pessimism inherent in cause-based mortality forecasts is derived. Second, it is shown that the pessimism of cause-based forecasts can be approximated using

This paper describes a model which relates fertility to partner availability, an aspect of relative cohort size. Partner availability is affected by the tendency for males to reproduce at a later age than females. For women born at a time of rising birth rates, there is a shortage of slightly older men as potential partners. Women born when birthrates are falling enjoy a surplus of older men from which

"We develop a new model of bivariate survival based on the notion of correlated individual frailty. We analyze the properties of this model and suggest a new approach to the analysis of bivariate data that does not require a parametric specification--but permits estimation--of the form of the hazard function for individuals. We empirically demonstrate the advantages of the model in the statistical

"This paper deals with the estimation of single equation models in which the counts are regressed on a set of observed individual characteristics such as age, gender, or nationality.... We propose a generalized event count model to simultaneously allow for a wide class of count data models and account for over- and underdispersion. This model is successfully applied to German data on fertility, divorces

"This paper provides a geometric-mean solution to the consistency problem of multidimensional demographic projection models, based on the constrained minimization of an entropy function. A comparison with the existing harmonic-mean solution yields many similarities and almost no differences....However, one major advantage of the geometric mean is that its corresponding distance function is firmly based

"For nearly 200 years actuaries, statisticians, and demographers have sought to summarize the age pattern of mortality rates by means of a limited number of parameters. Such 'model schedules' have also been useful in representing schedules of rates other than mortality....This paper illustrates a particular general functional form for such model schedules: the multiexponential function. It discusses

"Mortality data from the Netherlands are analyzed using recently developed statistical methods in the field of extreme value theory. It is shown that there is a finite age limit. A 95% confidence interval for the age limit is 113-124 years. The results suggest differences between men and women. The suggested hypotheses could be tested on a larger data set." (SUMMARY IN FRE)

"The purpose of this paper is to explain the interprefectural migrations at marriage in Japan by personal factors and ecological variables, using a multivariate statistical model called the nested logit model....The research is based on the micro data from a national survey on the life-course migration history of household heads and spouses, conducted in 1986 by the Institute of Population Problems

"One problem that researchers face in analyzing the survival times of groups of related individuals is selecting how the distribution of frailty--an unobserved (or not adequately observed) random factor--should be specified. Several distributions have received attention--for instance, the gamma distribution and a nonparametric N-point, discrete probability distribution. Researchers have selected these

The authors consider a demo-economic model where the economy consists of two sectors ("hunting and farming" and "industry"), and both sectors depend directly or indirectly on the explanation of a renewable resource. The primary sector harvests a renewable resource (fish, corn, or wood) which is used as the input into industrial production, the secondary sector of our economy. Labor is divided up between

"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the teacher/student ratio imply nonlinearities which are substantial enough to generate erratic behaviour of the time paths. The main message is that chaos in educational planning may result

"A fundamental shortcoming of classic stable population theory is its failure to handle populations differentiated by sex. The classic theory is linear while the two-sex problem is inherently nonlinear. Previous two-sex investigations have focused on equilibrium conditions rather than dynamics, and ignored competition between age groups for marriage partners. This study makes a start at analyzing dynamics

Several countries have attempted to change human fertility through economic incentives. This paper presents simple mathematical models of the participation of couples in a locally funded program of economic incentives. The models take as a springboard China's one-child program. Localities with low per capita incentives attract few couples to the program, while localities with high incentives attract

"In this paper we consider the simplest and most widely used demographic feedback model, the birth-response cohort feedback model. In the case of symmetric net maternity, we put the model into a form in which one of the rare global bifurcation theorems in the mathematical literature can be brought to bear. As a consequence, we prove that the model has solutions with period exactly twice the mean age

The Malthus-Boserup explanatory framework is revisited from the point of view of viability theory. Instead of imposing a univocal relationship between population pressure and level of knowledge, the way technology will change is not determined, it is only constrained. This leads to regard any situation as associated to a set of reachable futures. When no possibility is left for systems to avoid extinction

"Observed populations differ greatly in the speed with which they approach the stable form, but what determines rates of convergence is not fully understood.... Here we examine the trajectory to stability, derive a mathematical expression for the force of convergence, and provide an approximate relationship in terms of the mean and variance of the stable net maternity function." Trajectories for Japan

"We present a mortality model where nationally representative survey data on risk factor distributions are combined with data on cohort mortality rates to increase information, i.e., a fixed marginal risk factor distribution is combined with a cohort model representing unobserved individual risk heterogeneity. The model is applied to lung cancer mortality in nine U.S. white male cohorts aged 30 to

"In this paper, we consider crossovers of demographic density distributions from...populations that have the same fertility and mortality rates. We focus on observed populations and their associated stationary and stable models, and on proportional distributions of persons, births, deaths and reproductive values.... Three different populations were selected to represent a range of demographic behavior

"In this paper, we use simulation models to demonstrate the complexity of the relationship between the marriage selection process and the resulting RMRs [relative mortality ratios]. In particular, we show that marriage selection alone can produce a relative mortality ratio which remains large and relatively constant at ages far beyond the marriage span....Our general objective...is to determine the

Significant research attention has been given to historical patterns of marital fertility transitions in currently industrialized countries. Specifically, studies consider the time of the onset of fertility decline and its distribution among populations or population subgroups; the distribution of pre-decline parital fertility levels; and/or the rate of marital fertility decline. Analyses of pre-decline

"Formulas are derived for the effect that a slight change in the occurrence/exposure rate of the multidimensional projection model has on the elements of the population vector. The projection model classifies the population by sex, age, and marital status. The model includes a two-sex algorithm in order to ensure consistency between numbers of male and female marriages, number of divorces for the two

The author presents a method for estimating the age distribution of a population under varying vital statistics. "Some mathematical aspects of the method, as well as its applicability, will be discussed and numerical simulation will be run to illustrate the results and to compare the method with the traditional estimate of stable population theory...."

"In this paper we outline and evaluate a nine-parameter version of the Heligman-Pollard formula. In our applications, using mortality data for five European countries we found that this version provides closer fits to empirical mortality data than the classical eight-parameter formula, thus eliminating a source of systematic error in this latter formula."