Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate t...In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.展开更多
The Negative Binomial Multiple Change Point Algorithm is a hybrid change detection and estimation approach that works well for overdispersed and equidispersed count data. This simulation study assesses the performance...The Negative Binomial Multiple Change Point Algorithm is a hybrid change detection and estimation approach that works well for overdispersed and equidispersed count data. This simulation study assesses the performance of the NBMCPA under varying sample sizes and locations of true change points. Various performance metrics are calculated based on the change point estimates and used to assess how well the model correctly identifies change points. Errors in estimation of change points are obtained as absolute deviations of known change points from the change points estimated under the algorithm. Algorithm robustness is evaluated through error analysis and visualization techniques including kernel density estimation and computation of metrics such as change point location accuracy, precision, sensitivity and false positive rate. The results show that the model consistently detects change points that are present and does not erroneously detect changes where there are none. Change point location accuracy and precision of the NBMCPA increases with sample size, with best results for medium and large samples. Further model accuracy and precision are highest for changes located in the middle of the dataset compared to changes located in the periphery.展开更多
In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackl...In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackled by the NB component）, unobserved heterogeneity and spatial autocorrelation （captured by the CAR process）, using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic （AADT） per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.展开更多
For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state ...For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.展开更多
By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we...By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.展开更多
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schr?dinger cat states in a certa...We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schr?dinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.展开更多
Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function(WF) for the squeezed negative binomial state(SNBS) and the analytical evolution law of density operator...Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function(WF) for the squeezed negative binomial state(SNBS) and the analytical evolution law of density operator in the amplitude decay channel.The results show that the analytical WF is related to the square of the module of single-variable Hermite polynomials, which leads to a new two-variable special function and its generating function, and the parameters s and γplay opposite roles in the WF distributions.Besides, after undergoing this channel, the initial pure SNBS evolves into a new mixed state related to two operator Hermite polynomials within normal ordering, and fully loses its nonclassicality and decays to vacuum at long decay time.展开更多
In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering mal...In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering malicious reputation information. However,few have discussed the reputation direct update. In this paper,based on sound statistical theories,a negative binominal distribution method in the reputation direct update for WSNs is proposed. Results show that the proposed method is more suitable and time-saving for the reputation update of the resource constraint WSNs and can improve the computation power efficiency as well.展开更多
The purpose of this study is to compare a negative binomial distribution with a negative binomial—Lindley by using stochastic orders. We characterize the comparisons in usual stochastic order, likelihood ratio order,...The purpose of this study is to compare a negative binomial distribution with a negative binomial—Lindley by using stochastic orders. We characterize the comparisons in usual stochastic order, likelihood ratio order, convex order, expectation order and uniformly more variable order based on theorem and some numerical example of comparisons between negative binomial random variable and negative binomial—Lindley random variable.展开更多
Pasteuria penetrans controls root knots nematodes （Meloidogyne spp.） either by preventing invasion or by causing female sterility. The greatest control effect ofP. penetrans occurred when an efficient quantity ofP. ...Pasteuria penetrans controls root knots nematodes （Meloidogyne spp.） either by preventing invasion or by causing female sterility. The greatest control effect ofP. penetrans occurred when an efficient quantity ofP. penetrans spores attached to nematodes cuticle. The number of spores attaching to J2s within a given time increased with increasing the time of attachment. Based to that, we produced attachment data in vitro recorded encumbered nematodes 1, 3, 6 and 9 h after placing nematodes in a standard P. penetrans spore suspensions. From the count data obtained we modeled P. penetrans attachment using the Poisson and the negative binomial distribution. Attachment count data observed to be over dispersed with respect to high numbers of spores sticks on each J2 after at 6 and 9 h after spores application. We concluded that negative binomial distribution was shown to be the most appropriate model to fit the observed data sets considering that P. penetrans spores are clumped.展开更多
We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process ca...We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.展开更多
The rise of non-marital fertility, which seems to defy the Bongaarts model by decoupling marriage from fertility, has become a subject of interest in both the developed and developing world. Consequences of non-marita...The rise of non-marital fertility, which seems to defy the Bongaarts model by decoupling marriage from fertility, has become a subject of interest in both the developed and developing world. Consequences of non-marital fertility are mostly negative particularly in developing countries. In Namibia, although premarital childbearing has been reported to be high and increasing, no studies have explicitly analyzed factors influencing non-marital fertility. This paper uses data from the 2006/7 Namibia DHS to establish the determinants of non-marital fertility among women by applying a two-part model, with one part to describe the presence of non-marital birth and the other part to explain its intensity （number of children born）. Using the number of children ever born as an outcome, we explored various count data models. Based on the Voung statistics model comparison, we settled for the Hurdle logit Negative Binomial regression to model the number of non-marital births. Non-marital fertility in Namibia is associated with the age, with young women likely to have lower fertility compared to older women. Women with secondary or higher education had lower fertility compared those with no formal education. Findings also show that rural women higher fertility propensity compared to their urban counterparts even though there was no significant difference in fertility intensity. With regard to socio-economic status, fertility intensity decreased as the women got richer. Intervention efforts should focus on promoting education among girls and women especially in rural areas to improve their socio-economic status, reduce teenage pregnancy and non-marital fertility.展开更多
In the area of time series modelling, several applications are encountered in real-life that involve analysis of count time series data. The distribution characteristics and dependence structure are the major issues t...In the area of time series modelling, several applications are encountered in real-life that involve analysis of count time series data. The distribution characteristics and dependence structure are the major issues that arise while specifying a modelling strategy to handle the analysis of those kinds of data. Owing to the numerous applications there is a need to develop models that can capture these features. However, accounting for both aspects simultaneously presents complexities while specifying a modeling strategy. In this paper, an alternative statistical model able to deal with issues of discreteness, overdispersion, serial correlation over time is proposed. In particular, we adopt a branching mechanism to develop a first-order stationary negative binomial autoregressive model. Inference is based on maximum likelihood estimation and a simulation study is conducted to evaluate the performance of the proposed approach. As an illustration, the model is applied to a real-life dataset in crime analysis.展开更多
Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to compl...Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.Methods The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model, negative binomial (NB) model, zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and O test were used to identify over-dispersed data, and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.Results Of all 78 307 respondents, 38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98, and the standard deviation was 3.72. The statistic O in over-dispersion test was 720.995 (P<0.001); the estimated alpha was 0.618 (95% CI: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519), the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455),indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age, sex, occupation, smoking, alcohol drinking, ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex, occupation, smoking, alcohol drinking, ethnicity, marital status and obesity had significant effect on the severity of sub-health.Conclusions All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.展开更多
The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dip...The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.展开更多
Negative binomial regression is a powerful technique for modeling count data,particularly when dealing with overdispersion.However,estimating the parameters for large-dimensional sparse models is challenging due to th...Negative binomial regression is a powerful technique for modeling count data,particularly when dealing with overdispersion.However,estimating the parameters for large-dimensional sparse models is challenging due to the complexity of optimizing the mean and dispersion parameter of the negative binomial distribution.To address this issue,the authors propose a novel approach that employs two iterations of the majorize-minimize(MM)algorithm,one for estimating the dispersion parameter and the other for estimating the mean parameters.These approaches improve the convergence speed and stability of the algorithm.The authors also use group penalty for variable selection,which enhances the accuracy and efficiency of the algorithm.The proposed method provides an explicit solution,simplifies the iteration process,and maintains good stability while ensuring algorithm convergence.Furthermore,the authors apply the proposed algorithm to the zero-inflated model and demonstrate its promising predictive performance on specific data sets.The research has important implications for count data modeling and analysis in various fields,such as data mining,machine learning,and bioinformatics.展开更多
As the world grapples with increasing environmental challenges,innovative technologies are essential for promoting sustainability and accountability.This study examined the impact of environmental performance indices(...As the world grapples with increasing environmental challenges,innovative technologies are essential for promoting sustainability and accountability.This study examined the impact of environmental performance indices(EPIs)on the growth and investment trends of blockchain-based sustainability-focused companies in 15 countries(Belgium,Czechia,Denmark,Estonia,Finland,France,Germany,Italy,Norway,Poland,Sweden,Spain,Switzerland,the United Kingdom,and the United States)from Europe and America during 2010-2022.This study used the negative binomial regression model to assess the relationship between EPIs and blockchain-based sustainability-focused companies based on the data from the CrunchBase and EarthData.Results indicated that in ecosystem vitality,national terrestrial biome protection efforts were negatively correlated the formation of blockchain-based sustainability-focused companies,while global terrestrial biome protection efforts and marine protected areas had a positive impact on the formation of these companies and the number of funding rounds.In environmental health,PM2.5 exposure had a positive impact on the number of funding rounds.Conversely,pollutants such as sulfur dioxide(SO_(2))and ocean plastics deterred the formation of blockchain-based sustainability-focused companies and reduced the number of funding rounds.In climate change performance,adjusted emission growth rate for carbon dioxide(CO_(2)),adjusted emission growth rate for F-gases,and adjusted emission growth rate for black carbon had a significantly positive impact on the formation of blockchain-based sustainability-focused companies.Conversely,adjusted emission growth rate for Nitrous Oxide(N_(2)O)and projected greenhouse gas emissions in 2050 negatively affected the formation of these companies.These findings highlight the dual role of EPIs as driving factors and barriers in the development and investment of blockchain-based sustainability-focused companies in countries from Europe and America.展开更多
In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial ...In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.展开更多
In this paper we extend and improve some results of the large deviation for random sums of random variables. Let {Xn;n 〉 1} be a sequence of non-negative, independent and identically distributed random variables with...In this paper we extend and improve some results of the large deviation for random sums of random variables. Let {Xn;n 〉 1} be a sequence of non-negative, independent and identically distributed random variables with common heavy-tailed distribution function F and finite mean μ ∈R^＋, {N（n）; n ≥0} be a sequence of negative binomial distributed random variables with a parameter p C （0, 1）, n ≥ 0, let {M（n）; n ≥ 0} be a Poisson process with intensity λ 〉 0. Suppose {N（n）; n ≥ 0}, {Xn; n≥1} and {M（n）; n ≥ 0} are mutually independent. Write S（n） =N（n）∑i=1 Xi-cM（n）.Under the assumption F ∈ C, we prove some large deviation results. These results can be applied to certain problems in insurance and finance.展开更多
文摘Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
文摘In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.
文摘The Negative Binomial Multiple Change Point Algorithm is a hybrid change detection and estimation approach that works well for overdispersed and equidispersed count data. This simulation study assesses the performance of the NBMCPA under varying sample sizes and locations of true change points. Various performance metrics are calculated based on the change point estimates and used to assess how well the model correctly identifies change points. Errors in estimation of change points are obtained as absolute deviations of known change points from the change points estimated under the algorithm. Algorithm robustness is evaluated through error analysis and visualization techniques including kernel density estimation and computation of metrics such as change point location accuracy, precision, sensitivity and false positive rate. The results show that the model consistently detects change points that are present and does not erroneously detect changes where there are none. Change point location accuracy and precision of the NBMCPA increases with sample size, with best results for medium and large samples. Further model accuracy and precision are highest for changes located in the middle of the dataset compared to changes located in the periphery.
基金The National Science Foundation by Changjiang Scholarship of Ministry of Education of China(No.BCS-0527508)the Joint Research Fund for Overseas Natural Science of China(No.51250110075)+1 种基金the Natural Science Foundation of Jiangsu Province(No.SBK200910046)the Postdoctoral Science Foundation of Jiangsu Province(No.0901005C)
文摘In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackled by the NB component）, unobserved heterogeneity and spatial autocorrelation （captured by the CAR process）, using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic （AADT） per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 112470009)
文摘For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.
基金the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
文摘We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schr?dinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.
基金Project supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2016AM03 and ZR2017MA011)
文摘Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function(WF) for the squeezed negative binomial state(SNBS) and the analytical evolution law of density operator in the amplitude decay channel.The results show that the analytical WF is related to the square of the module of single-variable Hermite polynomials, which leads to a new two-variable special function and its generating function, and the parameters s and γplay opposite roles in the WF distributions.Besides, after undergoing this channel, the initial pure SNBS evolves into a new mixed state related to two operator Hermite polynomials within normal ordering, and fully loses its nonclassicality and decays to vacuum at long decay time.
基金supported by the National Natural Science Foundation of China under Grant No. 6107311
文摘In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering malicious reputation information. However,few have discussed the reputation direct update. In this paper,based on sound statistical theories,a negative binominal distribution method in the reputation direct update for WSNs is proposed. Results show that the proposed method is more suitable and time-saving for the reputation update of the resource constraint WSNs and can improve the computation power efficiency as well.
文摘The purpose of this study is to compare a negative binomial distribution with a negative binomial—Lindley by using stochastic orders. We characterize the comparisons in usual stochastic order, likelihood ratio order, convex order, expectation order and uniformly more variable order based on theorem and some numerical example of comparisons between negative binomial random variable and negative binomial—Lindley random variable.
文摘Pasteuria penetrans controls root knots nematodes （Meloidogyne spp.） either by preventing invasion or by causing female sterility. The greatest control effect ofP. penetrans occurred when an efficient quantity ofP. penetrans spores attached to nematodes cuticle. The number of spores attaching to J2s within a given time increased with increasing the time of attachment. Based to that, we produced attachment data in vitro recorded encumbered nematodes 1, 3, 6 and 9 h after placing nematodes in a standard P. penetrans spore suspensions. From the count data obtained we modeled P. penetrans attachment using the Poisson and the negative binomial distribution. Attachment count data observed to be over dispersed with respect to high numbers of spores sticks on each J2 after at 6 and 9 h after spores application. We concluded that negative binomial distribution was shown to be the most appropriate model to fit the observed data sets considering that P. penetrans spores are clumped.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB922103)the National Natural Science Foundation of China(Grant Nos.11175113,11274104,and 11404108)the Natural Science Foundation of Hubei Province,China(Grant No.2011CDA021)
文摘We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.
文摘The rise of non-marital fertility, which seems to defy the Bongaarts model by decoupling marriage from fertility, has become a subject of interest in both the developed and developing world. Consequences of non-marital fertility are mostly negative particularly in developing countries. In Namibia, although premarital childbearing has been reported to be high and increasing, no studies have explicitly analyzed factors influencing non-marital fertility. This paper uses data from the 2006/7 Namibia DHS to establish the determinants of non-marital fertility among women by applying a two-part model, with one part to describe the presence of non-marital birth and the other part to explain its intensity （number of children born）. Using the number of children ever born as an outcome, we explored various count data models. Based on the Voung statistics model comparison, we settled for the Hurdle logit Negative Binomial regression to model the number of non-marital births. Non-marital fertility in Namibia is associated with the age, with young women likely to have lower fertility compared to older women. Women with secondary or higher education had lower fertility compared those with no formal education. Findings also show that rural women higher fertility propensity compared to their urban counterparts even though there was no significant difference in fertility intensity. With regard to socio-economic status, fertility intensity decreased as the women got richer. Intervention efforts should focus on promoting education among girls and women especially in rural areas to improve their socio-economic status, reduce teenage pregnancy and non-marital fertility.
文摘In the area of time series modelling, several applications are encountered in real-life that involve analysis of count time series data. The distribution characteristics and dependence structure are the major issues that arise while specifying a modelling strategy to handle the analysis of those kinds of data. Owing to the numerous applications there is a need to develop models that can capture these features. However, accounting for both aspects simultaneously presents complexities while specifying a modeling strategy. In this paper, an alternative statistical model able to deal with issues of discreteness, overdispersion, serial correlation over time is proposed. In particular, we adopt a branching mechanism to develop a first-order stationary negative binomial autoregressive model. Inference is based on maximum likelihood estimation and a simulation study is conducted to evaluate the performance of the proposed approach. As an illustration, the model is applied to a real-life dataset in crime analysis.
基金supported by the Basic Performance Key Project,the Ministry of Science and Technology of the People’s Republic of China(No.2006FY110300)
文摘Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.Methods The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model, negative binomial (NB) model, zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and O test were used to identify over-dispersed data, and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.Results Of all 78 307 respondents, 38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98, and the standard deviation was 3.72. The statistic O in over-dispersion test was 720.995 (P<0.001); the estimated alpha was 0.618 (95% CI: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519), the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455),indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age, sex, occupation, smoking, alcohol drinking, ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex, occupation, smoking, alcohol drinking, ethnicity, marital status and obesity had significant effect on the severity of sub-health.Conclusions All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB922103)the National Natural Science Foundation of China(Grant Nos.11274104 and 11404108)
文摘The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.72111530199,12231017 and 72293573in part by the Natural Science Foundation of Anhui Province of China under Grant No.2108085J02。
文摘Negative binomial regression is a powerful technique for modeling count data,particularly when dealing with overdispersion.However,estimating the parameters for large-dimensional sparse models is challenging due to the complexity of optimizing the mean and dispersion parameter of the negative binomial distribution.To address this issue,the authors propose a novel approach that employs two iterations of the majorize-minimize(MM)algorithm,one for estimating the dispersion parameter and the other for estimating the mean parameters.These approaches improve the convergence speed and stability of the algorithm.The authors also use group penalty for variable selection,which enhances the accuracy and efficiency of the algorithm.The proposed method provides an explicit solution,simplifies the iteration process,and maintains good stability while ensuring algorithm convergence.Furthermore,the authors apply the proposed algorithm to the zero-inflated model and demonstrate its promising predictive performance on specific data sets.The research has important implications for count data modeling and analysis in various fields,such as data mining,machine learning,and bioinformatics.
文摘As the world grapples with increasing environmental challenges,innovative technologies are essential for promoting sustainability and accountability.This study examined the impact of environmental performance indices(EPIs)on the growth and investment trends of blockchain-based sustainability-focused companies in 15 countries(Belgium,Czechia,Denmark,Estonia,Finland,France,Germany,Italy,Norway,Poland,Sweden,Spain,Switzerland,the United Kingdom,and the United States)from Europe and America during 2010-2022.This study used the negative binomial regression model to assess the relationship between EPIs and blockchain-based sustainability-focused companies based on the data from the CrunchBase and EarthData.Results indicated that in ecosystem vitality,national terrestrial biome protection efforts were negatively correlated the formation of blockchain-based sustainability-focused companies,while global terrestrial biome protection efforts and marine protected areas had a positive impact on the formation of these companies and the number of funding rounds.In environmental health,PM2.5 exposure had a positive impact on the number of funding rounds.Conversely,pollutants such as sulfur dioxide(SO_(2))and ocean plastics deterred the formation of blockchain-based sustainability-focused companies and reduced the number of funding rounds.In climate change performance,adjusted emission growth rate for carbon dioxide(CO_(2)),adjusted emission growth rate for F-gases,and adjusted emission growth rate for black carbon had a significantly positive impact on the formation of blockchain-based sustainability-focused companies.Conversely,adjusted emission growth rate for Nitrous Oxide(N_(2)O)and projected greenhouse gas emissions in 2050 negatively affected the formation of these companies.These findings highlight the dual role of EPIs as driving factors and barriers in the development and investment of blockchain-based sustainability-focused companies in countries from Europe and America.
基金supported by National Natural Science Foundation of China(Nos.11871027,11731015)Science and Technology Developing Plan of Jilin Province(No.20170101057JC)Cultivation Plan for Excellent Young Scholar Candidates of Jilin University.
文摘In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.
文摘In this paper we extend and improve some results of the large deviation for random sums of random variables. Let {Xn;n 〉 1} be a sequence of non-negative, independent and identically distributed random variables with common heavy-tailed distribution function F and finite mean μ ∈R^＋, {N（n）; n ≥0} be a sequence of negative binomial distributed random variables with a parameter p C （0, 1）, n ≥ 0, let {M（n）; n ≥ 0} be a Poisson process with intensity λ 〉 0. Suppose {N（n）; n ≥ 0}, {Xn; n≥1} and {M（n）; n ≥ 0} are mutually independent. Write S（n） =N（n）∑i=1 Xi-cM（n）.Under the assumption F ∈ C, we prove some large deviation results. These results can be applied to certain problems in insurance and finance.
