Pub Date : 2022-04-19DOI: 10.1080/08898480.2022.2029074
N. Bonneuil, E. Fursa
ABSTRACT Seasonal variations in age class sizes involve those of births and those of mortality across ages. They affect censuses and, consequently, rates involving numbers by age. As their analytical expression becomes inextricable, a simulation of aging cohorts by months of age shows that mortality oscillations for human populations are not sufficient to prevent age classes from oscillating approximately like associated births, contrary to what previous literature suggests. The amplification converges after damping, and the level reached depends on the amplification of mortality oscillations relative to births between 0 and 6 months of age. The damping rate depends mainly on the amplification of the mortality of 0–5 months compared to births. The application to 1896 South Russian data shows that age class sizes vary during the year like the births of the associated cohorts and that the numbers counted at the census vary strongly according to the month of the census.
{"title":"Seasonal fluctuations of age classes, with application to South Russia, 1896-1897","authors":"N. Bonneuil, E. Fursa","doi":"10.1080/08898480.2022.2029074","DOIUrl":"https://doi.org/10.1080/08898480.2022.2029074","url":null,"abstract":"ABSTRACT Seasonal variations in age class sizes involve those of births and those of mortality across ages. They affect censuses and, consequently, rates involving numbers by age. As their analytical expression becomes inextricable, a simulation of aging cohorts by months of age shows that mortality oscillations for human populations are not sufficient to prevent age classes from oscillating approximately like associated births, contrary to what previous literature suggests. The amplification converges after damping, and the level reached depends on the amplification of mortality oscillations relative to births between 0 and 6 months of age. The damping rate depends mainly on the amplification of the mortality of 0–5 months compared to births. The application to 1896 South Russian data shows that age class sizes vary during the year like the births of the associated cohorts and that the numbers counted at the census vary strongly according to the month of the census.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60023922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-19DOI: 10.1080/08898480.2021.1997466
Kanisa Chodjuntug, Nuanpan Lawson
ABSTRACT Air pollution in Bangkok, Thailand, is mainly due to fine particles emitted in exhaust gases. However, many data on fine particle concentrations are missing, a fact which may bias the statistics. Exponential-type imputation minimizing the mean square error allows for estimating the missing values of these concentrations and provides an estimate with smaller mean square error of the mean concentration levels. The bias and mean square error of the proposed estimator are calculated. Simulation shows that the relative efficiency is 5% higher up to 50 observations, 12% higher for 100 observations, and 25% higher for 200 observations. Application to the measurement of fine particle concentration in Bangkok yields a mean square error of 0.73 micrograms per cubic meter squared, for a mean level of 47.40 micrograms per cubic meter, while the mean square error by the best alternative estimator selected is 0.90 micrograms per cubic meter squared, for a mean level of 48.20 micrograms per cubic meter.
{"title":"Imputation for estimating the population mean in the presence of nonresponse, with application to fine particle density in Bangkok","authors":"Kanisa Chodjuntug, Nuanpan Lawson","doi":"10.1080/08898480.2021.1997466","DOIUrl":"https://doi.org/10.1080/08898480.2021.1997466","url":null,"abstract":"ABSTRACT Air pollution in Bangkok, Thailand, is mainly due to fine particles emitted in exhaust gases. However, many data on fine particle concentrations are missing, a fact which may bias the statistics. Exponential-type imputation minimizing the mean square error allows for estimating the missing values of these concentrations and provides an estimate with smaller mean square error of the mean concentration levels. The bias and mean square error of the proposed estimator are calculated. Simulation shows that the relative efficiency is 5% higher up to 50 observations, 12% higher for 100 observations, and 25% higher for 200 observations. Application to the measurement of fine particle concentration in Bangkok yields a mean square error of 0.73 micrograms per cubic meter squared, for a mean level of 47.40 micrograms per cubic meter, while the mean square error by the best alternative estimator selected is 0.90 micrograms per cubic meter squared, for a mean level of 48.20 micrograms per cubic meter.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49068938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-27DOI: 10.1080/08898480.2021.1996822
Shuo Wang, Wangxue Chen, Meng Chen, Ya Zhou
ABSTRACT Maximum ranked set sampling with unequal samples is a sampling procedure used to reduce the error of ranking of observations and increase the efficiency of statistical inference. It is used for maximum likelihood estimation of the location and shape parameters of the inverse Gaussian distribution. Its asymptotic efficiency is at least 1.4 times higher than those of estimators based on simple random sampling. It is useful in reliability studies and in Bayesian statistics involving the inverse Gaussian distribution.
{"title":"Maximum likelihood estimation of the parameters of the inverse Gaussian distribution using maximum rank set sampling with unequal samples","authors":"Shuo Wang, Wangxue Chen, Meng Chen, Ya Zhou","doi":"10.1080/08898480.2021.1996822","DOIUrl":"https://doi.org/10.1080/08898480.2021.1996822","url":null,"abstract":"ABSTRACT Maximum ranked set sampling with unequal samples is a sampling procedure used to reduce the error of ranking of observations and increase the efficiency of statistical inference. It is used for maximum likelihood estimation of the location and shape parameters of the inverse Gaussian distribution. Its asymptotic efficiency is at least 1.4 times higher than those of estimators based on simple random sampling. It is useful in reliability studies and in Bayesian statistics involving the inverse Gaussian distribution.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49053538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-23DOI: 10.1080/08898480.2021.1988351
Igor Lazov, Petar Lazov
ABSTRACT A population is modeled by a birth-death process in a finite state space. Its stationary distribution is indexed by its birth-death ratio. A sample of values taken by the population size has an elastic sample mean (mean of the observations), an additional sample mean (mean of the logarithms of the observations transformed by a given function), and a synchronizing sample mean (combination of the previous means). When the last two means are zero, then, by definition, information is linear in population size. This is only the case when the population size is geometrically distributed. Equalizing the entropy of a distribution to the entropy calculated on any sample involves the three sample means and allows for estimating the birth-death ratio. Only in the case of information linear in population size, this procedure reduces to maximum likelihood estimation, which involves only the elastic sample mean. The procedure is demonstrated on information that is no longer linear in population size, such as a binomial distribution of population size, where the last two means are not zero, but just equal, and a Pascal distribution and a Poisson distribution, where the last two means are neither zero nor equal.
{"title":"Entropy-based estimation of the birth-death ratio","authors":"Igor Lazov, Petar Lazov","doi":"10.1080/08898480.2021.1988351","DOIUrl":"https://doi.org/10.1080/08898480.2021.1988351","url":null,"abstract":"ABSTRACT A population is modeled by a birth-death process in a finite state space. Its stationary distribution is indexed by its birth-death ratio. A sample of values taken by the population size has an elastic sample mean (mean of the observations), an additional sample mean (mean of the logarithms of the observations transformed by a given function), and a synchronizing sample mean (combination of the previous means). When the last two means are zero, then, by definition, information is linear in population size. This is only the case when the population size is geometrically distributed. Equalizing the entropy of a distribution to the entropy calculated on any sample involves the three sample means and allows for estimating the birth-death ratio. Only in the case of information linear in population size, this procedure reduces to maximum likelihood estimation, which involves only the elastic sample mean. The procedure is demonstrated on information that is no longer linear in population size, such as a binomial distribution of population size, where the last two means are not zero, but just equal, and a Pascal distribution and a Poisson distribution, where the last two means are neither zero nor equal.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47313002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-30DOI: 10.1080/08898480.2021.1983323
Christine Brasic, Latimer Harris-Ward, F. Milner, Carlos Bustamante-Orellana, Jordy Cevallos-Chavez, L. Arriola
ABSTRACT Ingestion of lead-based ammunition is one of the leading causes of the mortality of bald eagles. Their primary source is unretrieved carrion contaminated with lead from hunters’ ammunition. Lead toxicity can have serious clinical consequences, including reduced fertility and consumption. A model with ordinary differential equations describes the dynamics of available contaminated carrion and the progression of eagles through stages of lead poisoning. Nonnegative solutions exist and equilibrium points are stable for certain parameter ranges. Sensitivity analysis shows that the bald eagle population in the Great Lakes region is primarily dependent on the rate of entry of contaminated carrion in the environment, more so than on retrieval or on the rate of treatment of eagles. Estimates of financial costs of each of these three measures show that the most effective measure is to find a substitute for lead cartridges.
{"title":"Lead toxicity in the bald eagle population of the Great Lakes region","authors":"Christine Brasic, Latimer Harris-Ward, F. Milner, Carlos Bustamante-Orellana, Jordy Cevallos-Chavez, L. Arriola","doi":"10.1080/08898480.2021.1983323","DOIUrl":"https://doi.org/10.1080/08898480.2021.1983323","url":null,"abstract":"ABSTRACT Ingestion of lead-based ammunition is one of the leading causes of the mortality of bald eagles. Their primary source is unretrieved carrion contaminated with lead from hunters’ ammunition. Lead toxicity can have serious clinical consequences, including reduced fertility and consumption. A model with ordinary differential equations describes the dynamics of available contaminated carrion and the progression of eagles through stages of lead poisoning. Nonnegative solutions exist and equilibrium points are stable for certain parameter ranges. Sensitivity analysis shows that the bald eagle population in the Great Lakes region is primarily dependent on the rate of entry of contaminated carrion in the environment, more so than on retrieval or on the rate of treatment of eagles. Estimates of financial costs of each of these three measures show that the most effective measure is to find a substitute for lead cartridges.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47594759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1080/08898480.2021.1976476
Branda Goncalves, Thiery E. Huillet
ABSTRACT Recurrence and transience conditions are made explicit in discrete-time Markov chain population models for which random stationary growth alternates with disastrous random life-taking events. These events either have moderate stationary magnitudes or lead to an abrupt population decline. The probability of their occurrence may or may not depend on the population size. These conditions are based on the existence or not of a “weak” carrying capacity, where “weak” means that the carrying capacity can be exceeded, temporarily. In this framework, the population is threatened with extinction, an event whose probability is expressed, as well as the law of the time remaining until this deadline. On the other hand, the population is also threatened by overpopulation, an event whose time to reach a given threshold is expressed, as well as the difference between the population size and the carrying capacity. The theory is that of extreme values for Markov chains and is based on the control of the spectral properties of the northwest truncation of the transition matrix of the original Markov chain with life-taking disasters. The article presents an extension to the case where the process of life-taking disasters is no longer geometric and to the case where the probability of occurrence of a disaster depends on the population size. Both the time to extinction and the time to a given threshold have geometrically decaying distribution tails. The use of the extremal Markov chain in the calculation of the time to overpopulation is innovative.
{"title":"Keeping random walks safe from extinction and overpopulation in the presence of life-taking disasters","authors":"Branda Goncalves, Thiery E. Huillet","doi":"10.1080/08898480.2021.1976476","DOIUrl":"https://doi.org/10.1080/08898480.2021.1976476","url":null,"abstract":"ABSTRACT Recurrence and transience conditions are made explicit in discrete-time Markov chain population models for which random stationary growth alternates with disastrous random life-taking events. These events either have moderate stationary magnitudes or lead to an abrupt population decline. The probability of their occurrence may or may not depend on the population size. These conditions are based on the existence or not of a “weak” carrying capacity, where “weak” means that the carrying capacity can be exceeded, temporarily. In this framework, the population is threatened with extinction, an event whose probability is expressed, as well as the law of the time remaining until this deadline. On the other hand, the population is also threatened by overpopulation, an event whose time to reach a given threshold is expressed, as well as the difference between the population size and the carrying capacity. The theory is that of extreme values for Markov chains and is based on the control of the spectral properties of the northwest truncation of the transition matrix of the original Markov chain with life-taking disasters. The article presents an extension to the case where the process of life-taking disasters is no longer geometric and to the case where the probability of occurrence of a disaster depends on the population size. Both the time to extinction and the time to a given threshold have geometrically decaying distribution tails. The use of the extremal Markov chain in the calculation of the time to overpopulation is innovative.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46636913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-30DOI: 10.1080/08898480.2021.1959817
H. Nasir, A. A. Mat Daud
ABSTRACT Population models of diabetes using ordinary differential equations are reviewed. They are refined by incorporating non-diabetics, prediabetics, low awareness prediabetics, awareness prediabetics, and awareness programs. However, they may involve products and fractions that do not reflect what is known about reality or ignore the presence of time lags in the development of diabetes. No model takes into account the limited medical treatments considered. This review shows the need to consider finer specifications of interactions, time delays, and budget constraints in epidemiological modeling of diabetes.
{"title":"Population models of diabetes mellitus by ordinary differential equations: a review","authors":"H. Nasir, A. A. Mat Daud","doi":"10.1080/08898480.2021.1959817","DOIUrl":"https://doi.org/10.1080/08898480.2021.1959817","url":null,"abstract":"ABSTRACT Population models of diabetes using ordinary differential equations are reviewed. They are refined by incorporating non-diabetics, prediabetics, low awareness prediabetics, awareness prediabetics, and awareness programs. However, they may involve products and fractions that do not reflect what is known about reality or ignore the presence of time lags in the development of diabetes. No model takes into account the limited medical treatments considered. This review shows the need to consider finer specifications of interactions, time delays, and budget constraints in epidemiological modeling of diabetes.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42390321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-26DOI: 10.1080/08898480.2021.1949923
U. Shahzad, I. Ahmad, I. Almanjahie, N. Koyuncu, M. Hanif
ABSTRACT The presence of extreme values in a data set reduces the efficiency of variance estimators. L-moments are based on the ordered form of a random variable to estimate the variance of the population. The two variance estimators are used for calibration to a stratified random sampling design and relying on an auxiliary variable. The proposed estimators use the properties of L-moments, such as the L-mean, also called L-location, the L-standard deviation, also called L-scaling, and the L-coefficient of variation, which is a measure of variation. The use of these properties allows for providing better estimators. A simulation proves the better efficiency of these estimators.
{"title":"Variance estimation based on L-moments and auxiliary information","authors":"U. Shahzad, I. Ahmad, I. Almanjahie, N. Koyuncu, M. Hanif","doi":"10.1080/08898480.2021.1949923","DOIUrl":"https://doi.org/10.1080/08898480.2021.1949923","url":null,"abstract":"ABSTRACT The presence of extreme values in a data set reduces the efficiency of variance estimators. L-moments are based on the ordered form of a random variable to estimate the variance of the population. The two variance estimators are used for calibration to a stratified random sampling design and relying on an auxiliary variable. The proposed estimators use the properties of L-moments, such as the L-mean, also called L-location, the L-standard deviation, also called L-scaling, and the L-coefficient of variation, which is a measure of variation. The use of these properties allows for providing better estimators. A simulation proves the better efficiency of these estimators.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/08898480.2021.1949923","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46208283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-09DOI: 10.1080/08898480.2021.1942654
E. Gayawan, Olamide Seyi Orunmoluyi, O. Adegboye
ABSTRACT Among children under five in Nigeria, in the year 2018, the prevalence of diarrhea was 13%, that of acute respiratory infections 3%, and that of stunting 37%. A shared-component model highlights geographic variations in the comorbidities of these diseases. The data are from the 2018 Nigeria Demographic and Health Survey. The majority of states in northern Nigeria presented clusters of higher risk for comorbidities of any pair of the three diseases. Compared with mothers with primary education or less, mothers with secondary education were 1.4 times less likely to have two or three of these diseases at the same time, and women with tertiary education 2.0 times less. Compared to childless women of the same age, mothers were 1.6 times less when aged 20–29, 1.9 times less when aged 30–39, and 2.0 times less when aged 40–49. Access to a protected water source reduced the risk by a factor of 1.3. Girls under age five were 1.2 times less likely than boys of that age to have two or three of these diseases at the same time. This factor was the same for breastfed children compared to those who were not breastfed.
{"title":"Geostatistical patterns of comorbidity of diarrhea, acute respiratory infection, and stunting among under-five children in Nigeria","authors":"E. Gayawan, Olamide Seyi Orunmoluyi, O. Adegboye","doi":"10.1080/08898480.2021.1942654","DOIUrl":"https://doi.org/10.1080/08898480.2021.1942654","url":null,"abstract":"ABSTRACT Among children under five in Nigeria, in the year 2018, the prevalence of diarrhea was 13%, that of acute respiratory infections 3%, and that of stunting 37%. A shared-component model highlights geographic variations in the comorbidities of these diseases. The data are from the 2018 Nigeria Demographic and Health Survey. The majority of states in northern Nigeria presented clusters of higher risk for comorbidities of any pair of the three diseases. Compared with mothers with primary education or less, mothers with secondary education were 1.4 times less likely to have two or three of these diseases at the same time, and women with tertiary education 2.0 times less. Compared to childless women of the same age, mothers were 1.6 times less when aged 20–29, 1.9 times less when aged 30–39, and 2.0 times less when aged 40–49. Access to a protected water source reduced the risk by a factor of 1.3. Girls under age five were 1.2 times less likely than boys of that age to have two or three of these diseases at the same time. This factor was the same for breastfed children compared to those who were not breastfed.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/08898480.2021.1942654","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47332651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-09DOI: 10.1080/08898480.2021.1941661
M. El Fatini, Mohamed El khalifi, R. Gerlach, R. Pettersson
ABSTRACT In a Covid-19 susceptible-infected-recovered-dead model with time-varying rates of transmission, recovery, and death, the parameters are constant in small time intervals. A posteriori parameters result from the Euler-Maruyama approximation for stochastic differential equations and from Bayes’ theorem. Parameter estimates and 10-day predictions are performed based on Moroccan and Italian Covid-19 data. Mean absolute errors and mean square errors indicate that predictions are of good quality.
{"title":"Bayesian forecast of the basic reproduction number during the Covid-19 epidemic in Morocco and Italy","authors":"M. El Fatini, Mohamed El khalifi, R. Gerlach, R. Pettersson","doi":"10.1080/08898480.2021.1941661","DOIUrl":"https://doi.org/10.1080/08898480.2021.1941661","url":null,"abstract":"ABSTRACT In a Covid-19 susceptible-infected-recovered-dead model with time-varying rates of transmission, recovery, and death, the parameters are constant in small time intervals. A posteriori parameters result from the Euler-Maruyama approximation for stochastic differential equations and from Bayes’ theorem. Parameter estimates and 10-day predictions are performed based on Moroccan and Italian Covid-19 data. Mean absolute errors and mean square errors indicate that predictions are of good quality.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/08898480.2021.1941661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47451107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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