Pub Date : 2023-01-05DOI: 10.1080/08898480.2022.2155415
F. Benassi, A. Naccarato, Meng Xu
ABSTRACT Taylor’s law states that the spatial variance of the population density varies as the power function of the mean population density. This law is tested on daily Covid-19 infection density for five periods between February 25, 2020 and March 15, 2021. The Italian provinces are grouped by geography into three ensembles. A simultaneous-equation model accounts for correlations between the ensembles, between Italian provinces within each ensemble, and for temporal autocorrelations. The selected periods show ensembles with all Taylor’s law slopes below 2 (reflecting State interventions at the national level), or all above 2 (reflecting interventions at the local level), or some ensembles above while others were below. Slope of Taylor’s law and average density trend indicate whether the infection density is highly concentrated in a few provinces (when the slope is greater than 2 with increasing density, and when the slope is less than 2 with decreasing density) or spread evenly among all provinces in an ensemble (when the slope is greater than 2 with decreasing density, and when the slope is less than 2 with increasing density), which allows the government and epidemiologists to design disease control policies for targeted provinces and ensembles in Italy.
{"title":"Daily Covid-19 infected population densities in Italian provinces follow Taylor’s law","authors":"F. Benassi, A. Naccarato, Meng Xu","doi":"10.1080/08898480.2022.2155415","DOIUrl":"https://doi.org/10.1080/08898480.2022.2155415","url":null,"abstract":"ABSTRACT Taylor’s law states that the spatial variance of the population density varies as the power function of the mean population density. This law is tested on daily Covid-19 infection density for five periods between February 25, 2020 and March 15, 2021. The Italian provinces are grouped by geography into three ensembles. A simultaneous-equation model accounts for correlations between the ensembles, between Italian provinces within each ensemble, and for temporal autocorrelations. The selected periods show ensembles with all Taylor’s law slopes below 2 (reflecting State interventions at the national level), or all above 2 (reflecting interventions at the local level), or some ensembles above while others were below. Slope of Taylor’s law and average density trend indicate whether the infection density is highly concentrated in a few provinces (when the slope is greater than 2 with increasing density, and when the slope is less than 2 with decreasing density) or spread evenly among all provinces in an ensemble (when the slope is greater than 2 with decreasing density, and when the slope is less than 2 with increasing density), which allows the government and epidemiologists to design disease control policies for targeted provinces and ensembles in Italy.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47606087","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 : 2022-12-05DOI: 10.1080/08898480.2022.2139072
U. Shahzad, I. Ahmad, N. Al-Noor, M. Hanif, I. Almanjahie
ABSTRACT Regression ratio mean estimators of a study variable are defined as the coefficients provided by the ordinary least-squares regression of on a given auxiliary variable . They can be improved by using the coefficient of variation and the coefficient of kurtosis of . The influence of outliers on the estimates of the population mean of is neutralized by calculating robust regression coefficients, obtained by the method of either least absolute deviations, Huber-M, Huber-MM, Hampel-M, Tukey-M, or adjusted least squares. These robust coefficients are used to estimate the population mean of under simple random sampling. Extension to systematic sampling—which is a probability sampling in which every element of the population has equal probability of inclusion to be drawn—using the coefficients provided by quantile regression—whose coefficients result from the minimization of the sum of absolute deviations rather than from the square deviations from the regression line—requires ratio estimators of the population mean of . The mean square errors of these estimators are expressed analytically. If the quantile regression coefficient is greater than the ratio of the covariance between the study and the auxiliary variables to the variance of the auxiliary variable minus a function of the mean or the coefficient of variation, skewness, or kurtosis of and , then the proposed robust quantile regression mean estimator of is more efficient than the ratio estimators in the presence of outliers under systematic sampling. The reason is that these estimators only use regression coefficients and not the ratio between the population mean and sample means of the auxiliary variable . The aforementioned condition occurs with the values of the case study. For empirical data of 176 forest strips, the proposed estimate of the volume of timber is over 30% more efficient than the ratio estimates based on quantile regression coefficients.
{"title":"Robust estimation of the population mean using quantile regression under systematic sampling","authors":"U. Shahzad, I. Ahmad, N. Al-Noor, M. Hanif, I. Almanjahie","doi":"10.1080/08898480.2022.2139072","DOIUrl":"https://doi.org/10.1080/08898480.2022.2139072","url":null,"abstract":"ABSTRACT Regression ratio mean estimators of a study variable are defined as the coefficients provided by the ordinary least-squares regression of on a given auxiliary variable . They can be improved by using the coefficient of variation and the coefficient of kurtosis of . The influence of outliers on the estimates of the population mean of is neutralized by calculating robust regression coefficients, obtained by the method of either least absolute deviations, Huber-M, Huber-MM, Hampel-M, Tukey-M, or adjusted least squares. These robust coefficients are used to estimate the population mean of under simple random sampling. Extension to systematic sampling—which is a probability sampling in which every element of the population has equal probability of inclusion to be drawn—using the coefficients provided by quantile regression—whose coefficients result from the minimization of the sum of absolute deviations rather than from the square deviations from the regression line—requires ratio estimators of the population mean of . The mean square errors of these estimators are expressed analytically. If the quantile regression coefficient is greater than the ratio of the covariance between the study and the auxiliary variables to the variance of the auxiliary variable minus a function of the mean or the coefficient of variation, skewness, or kurtosis of and , then the proposed robust quantile regression mean estimator of is more efficient than the ratio estimators in the presence of outliers under systematic sampling. The reason is that these estimators only use regression coefficients and not the ratio between the population mean and sample means of the auxiliary variable . The aforementioned condition occurs with the values of the case study. For empirical data of 176 forest strips, the proposed estimate of the volume of timber is over 30% more efficient than the ratio estimates based on quantile regression coefficients.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48451618","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 : 2022-12-05DOI: 10.1080/08898480.2022.2133850
Mehdi Bazyar, E. Deiri, E. Jamkhaneh
ABSTRACT The Moore-Bilikam distribution is convenient for survival analysis. The estimation of its parameters and its reliability function is performed by maximum likelihood, expectation-maximization, stochastic expectation-maximization, and the Bayesian method. The data are progressively censored of type II (samples are removed randomly from the experiment). Simulation shows that the expectation-maximization estimator of the parameter and the Bayesian-shrinkage estimator of the reliability function are the most efficient (with the minimum mean square error) when they are based on the Weibull and the Pareto distributions, which are specific cases of the Moore-Bilikam distribution. Bayesian and maximum likelihood estimations using the Moore-Bilikam distribution under type-II progressive censoring allow for fitting empirical failure times of an insulating fluid between two electrodes and the resistance of single carbon fibers. The associated reliability functions are estimated by each method.
{"title":"Parameter estimation for the Moore-Bilikam distribution under progressive type-II censoring, with application to failure times","authors":"Mehdi Bazyar, E. Deiri, E. Jamkhaneh","doi":"10.1080/08898480.2022.2133850","DOIUrl":"https://doi.org/10.1080/08898480.2022.2133850","url":null,"abstract":"ABSTRACT The Moore-Bilikam distribution is convenient for survival analysis. The estimation of its parameters and its reliability function is performed by maximum likelihood, expectation-maximization, stochastic expectation-maximization, and the Bayesian method. The data are progressively censored of type II (samples are removed randomly from the experiment). Simulation shows that the expectation-maximization estimator of the parameter and the Bayesian-shrinkage estimator of the reliability function are the most efficient (with the minimum mean square error) when they are based on the Weibull and the Pareto distributions, which are specific cases of the Moore-Bilikam distribution. Bayesian and maximum likelihood estimations using the Moore-Bilikam distribution under type-II progressive censoring allow for fitting empirical failure times of an insulating fluid between two electrodes and the resistance of single carbon fibers. The associated reliability functions are estimated by each method.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45185602","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 : 2022-12-05DOI: 10.1080/08898480.2022.2145790
Natthapat Thongsak, Nuanpan Lawson
ABSTRACT The proposed estimator of the population mean is based on a modification of the shape of the distribution of an auxiliary variable. If the theoretical correlation between the study and the auxiliary variables is less than a term that is proportional to the coefficient of variation of the auxiliary variable divided by the coefficient of variation of the study variable, then the modification of the distribution of the auxiliary variable reduces the bias and the mean square error of the estimator. A simulation confirms the analytical results. Application to air pollution data in Nan, Thailand, shows that on average, the biases of the estimators based on the modified auxiliary variable are reduced by 70% to 98% and the mean square errors by 91% to 100% compared to the estimators based on the unmodified auxiliary variable.
{"title":"Bias and mean square error reduction by changing the shape of the distribution of an auxiliary variable: application to air pollution data in Nan, Thailand","authors":"Natthapat Thongsak, Nuanpan Lawson","doi":"10.1080/08898480.2022.2145790","DOIUrl":"https://doi.org/10.1080/08898480.2022.2145790","url":null,"abstract":"ABSTRACT The proposed estimator of the population mean is based on a modification of the shape of the distribution of an auxiliary variable. If the theoretical correlation between the study and the auxiliary variables is less than a term that is proportional to the coefficient of variation of the auxiliary variable divided by the coefficient of variation of the study variable, then the modification of the distribution of the auxiliary variable reduces the bias and the mean square error of the estimator. A simulation confirms the analytical results. Application to air pollution data in Nan, Thailand, shows that on average, the biases of the estimators based on the modified auxiliary variable are reduced by 70% to 98% and the mean square errors by 91% to 100% compared to the estimators based on the unmodified auxiliary variable.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47319445","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 : 2022-12-02DOI: 10.1080/08898480.2022.2140561
E. Chernousova, O. Hryniv, S. Molchanov
ABSTRACT In a lattice population model, particles move randomly from one site to another as independent random walks, split into two offspring, or die. If duplication and mortality rates are equal and take the same value over all lattice sites, the resulting model is a critical branching random walk (characterized by a mean total number of offspring equal to ). There exists an asymptotical statistical equilibrium, also called steady state. In contrast, when duplication and mortality rates take independent random values drawn from a common nondegenerate distribution (so that the difference between duplication and mortality rates has nonzero variance), then the steady state no longer exists. Simultaneously, at all lattice sites, if the difference between duplication and mortality rates takes strictly positive values with strictly positive probability, the total number of particles grows exponentially. The lattice includes large connected sets where the duplication rate exceeds the mortality rate by a positive constant amount, and these connected sets provide the growth of the total population. This is the supercritical regime of branching processes. On the other hand, if the difference between duplication and mortality rates is almost surely negative or null except when it is almost surely zero, then the total number of particles vanishes asymptotically. The steady state can be reached only if the difference between duplication and mortality rates is almost surely zero.
{"title":"Branching random walk in a random time-independent environment","authors":"E. Chernousova, O. Hryniv, S. Molchanov","doi":"10.1080/08898480.2022.2140561","DOIUrl":"https://doi.org/10.1080/08898480.2022.2140561","url":null,"abstract":"ABSTRACT In a lattice population model, particles move randomly from one site to another as independent random walks, split into two offspring, or die. If duplication and mortality rates are equal and take the same value over all lattice sites, the resulting model is a critical branching random walk (characterized by a mean total number of offspring equal to ). There exists an asymptotical statistical equilibrium, also called steady state. In contrast, when duplication and mortality rates take independent random values drawn from a common nondegenerate distribution (so that the difference between duplication and mortality rates has nonzero variance), then the steady state no longer exists. Simultaneously, at all lattice sites, if the difference between duplication and mortality rates takes strictly positive values with strictly positive probability, the total number of particles grows exponentially. The lattice includes large connected sets where the duplication rate exceeds the mortality rate by a positive constant amount, and these connected sets provide the growth of the total population. This is the supercritical regime of branching processes. On the other hand, if the difference between duplication and mortality rates is almost surely negative or null except when it is almost surely zero, then the total number of particles vanishes asymptotically. The steady state can be reached only if the difference between duplication and mortality rates is almost surely zero.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44396689","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 : 2022-06-13DOI: 10.1080/08898480.2022.2075166
Guihua Hu, Ting Wen, Yuhuan Liu
ABSTRACT Post-enumeration surveys are used to assess the quality of censuses. To set up such a survey, the size of the sample to be surveyed must be determined. If the sample design requires several strata, the design effect, which is the ratio of the variance of the two-source estimator to the variance of the single-source estimator for a given sample size, allows an indirect calculation. Another method is to use the sampling variance formula for a given sample size. The sample must have a sufficient total number of geographic subdivisions that are too small. A complete calculation of the sample size is implemented on an example from the 2020 Chinese post-enumeration survey.
{"title":"Determining the sample size of a post-enumeration survey: The case of China, 2020","authors":"Guihua Hu, Ting Wen, Yuhuan Liu","doi":"10.1080/08898480.2022.2075166","DOIUrl":"https://doi.org/10.1080/08898480.2022.2075166","url":null,"abstract":"ABSTRACT Post-enumeration surveys are used to assess the quality of censuses. To set up such a survey, the size of the sample to be surveyed must be determined. If the sample design requires several strata, the design effect, which is the ratio of the variance of the two-source estimator to the variance of the single-source estimator for a given sample size, allows an indirect calculation. Another method is to use the sampling variance formula for a given sample size. The sample must have a sufficient total number of geographic subdivisions that are too small. A complete calculation of the sample size is implemented on an example from the 2020 Chinese post-enumeration survey.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42868144","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 : 2022-05-09DOI: 10.1080/08898480.2022.2043067
Liangping Qi, Guowei Zong
ABSTRACT To prove the existence of piecewise continuous solutions to a logistic quasi-periodic differential system with impulses (whose coefficients have rationally independent periods), this system is divided into a differential equation and a difference equation. The quasi-periodicity of a function is proved by showing that this function is the uniform limit of a series of trigonometric polynomials with a finite total number of frequencies. The asymptotically stable quasi-periodic positive and piecewise continuous solution is proved to exist and to be unique. Quasi-periodic variation of the environment leads to a quasi-periodic growth of the population size in the sense that the rationally independent frequencies of the system are also frequencies of the quasi-periodic solution. The positive solutions have a repeated behavior similar to that of the quasi-periodic solution for a sufficiently long time due to asymptotical stability. The separation of the continuous-discrete system into a differential equation and a difference equation is a method of proving the existence of a quasi-periodic solution with perturbed coefficients of the impulsive system.
{"title":"Positive piecewise continuous quasi-periodic solutions to logistic impulsive differential equations","authors":"Liangping Qi, Guowei Zong","doi":"10.1080/08898480.2022.2043067","DOIUrl":"https://doi.org/10.1080/08898480.2022.2043067","url":null,"abstract":"ABSTRACT To prove the existence of piecewise continuous solutions to a logistic quasi-periodic differential system with impulses (whose coefficients have rationally independent periods), this system is divided into a differential equation and a difference equation. The quasi-periodicity of a function is proved by showing that this function is the uniform limit of a series of trigonometric polynomials with a finite total number of frequencies. The asymptotically stable quasi-periodic positive and piecewise continuous solution is proved to exist and to be unique. Quasi-periodic variation of the environment leads to a quasi-periodic growth of the population size in the sense that the rationally independent frequencies of the system are also frequencies of the quasi-periodic solution. The positive solutions have a repeated behavior similar to that of the quasi-periodic solution for a sufficiently long time due to asymptotical stability. The separation of the continuous-discrete system into a differential equation and a difference equation is a method of proving the existence of a quasi-periodic solution with perturbed coefficients of the impulsive system.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44933773","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 : 2022-05-06DOI: 10.1080/08898480.2022.2055870
Siraj Muneer, A. Khalil, J. Shabbir
ABSTRACT To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated.
{"title":"Multivariate ratio exponential estimators of the population mean under stratified double sampling","authors":"Siraj Muneer, A. Khalil, J. Shabbir","doi":"10.1080/08898480.2022.2055870","DOIUrl":"https://doi.org/10.1080/08898480.2022.2055870","url":null,"abstract":"ABSTRACT To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49283697","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 : 2022-05-04DOI: 10.1080/08898480.2022.2051367
I. Elbaz
ABSTRACT Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson’s model describes the population dynamics of the Australian blowfly (Lucilia Cuprina). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, Lucilia Sericata, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: L. Sericata prefers warmer months, thus in summer, while L. Cuprina is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.
{"title":"Reduced oviposition period promotes blowfly population extinction in Nicholson’s model","authors":"I. Elbaz","doi":"10.1080/08898480.2022.2051367","DOIUrl":"https://doi.org/10.1080/08898480.2022.2051367","url":null,"abstract":"ABSTRACT Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson’s model describes the population dynamics of the Australian blowfly (Lucilia Cuprina). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, Lucilia Sericata, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: L. Sericata prefers warmer months, thus in summer, while L. Cuprina is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45320539","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 : 2022-05-03DOI: 10.1080/08898480.2022.2051988
H. Koç, Caner Tanış, T. Zaman
ABSTRACT Poisson regression is used to deal with count data. The Poisson regression ratio estimator of the population mean is extended from single to double sampling. This is made possible by the provision of the population mean of an auxiliary variable. The mean square errors of the proposed estimators are expressed up to the first order. Theoretical and numerical results demonstrate that the proposed double-sampling Poisson-regression ratio estimator has a lower mean square error than the double-ratio and the single-sampling estimator. For Covid-19, the minimum mean square errors yielded by the proposed estimator of the total number of cases are 0.095 cases per day and 67.8 cases, compared with 0.112 cases per day and 84.8 cases with the double-ratio estimator.
{"title":"Poisson regression-ratio estimators of the population mean under double sampling, with application to Covid-19","authors":"H. Koç, Caner Tanış, T. Zaman","doi":"10.1080/08898480.2022.2051988","DOIUrl":"https://doi.org/10.1080/08898480.2022.2051988","url":null,"abstract":"ABSTRACT Poisson regression is used to deal with count data. The Poisson regression ratio estimator of the population mean is extended from single to double sampling. This is made possible by the provision of the population mean of an auxiliary variable. The mean square errors of the proposed estimators are expressed up to the first order. Theoretical and numerical results demonstrate that the proposed double-sampling Poisson-regression ratio estimator has a lower mean square error than the double-ratio and the single-sampling estimator. For Covid-19, the minimum mean square errors yielded by the proposed estimator of the total number of cases are 0.095 cases per day and 67.8 cases, compared with 0.112 cases per day and 84.8 cases with the double-ratio estimator.","PeriodicalId":49859,"journal":{"name":"Mathematical Population Studies","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47025028","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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