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
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 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
Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
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
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
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
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
A Poisson regression model and a negative binomial regression model(NB model) are often used in areas such as medicine and economy,but rarely in the domestic forestry sector,especially in the forest fire forecasting.B...A Poisson regression model and a negative binomial regression model(NB model) are often used in areas such as medicine and economy,but rarely in the domestic forestry sector,especially in the forest fire forecasting.Based on the data of forest fire occurrences in Daxing’anling region in 1980- 2005,this paper profoundly analyzes the application conditions and test methods of the two models.The AIC method was used to check the fitting level of the models and the capability of the models for forecasting forest fires was discussed.This study provided necessary theoretical basis and data support for the application of the two models in the field of forestry in China.展开更多
The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion (i.e., variance is larger than mean) and a high frequency of zero counts. In this study, we used six gene...The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion (i.e., variance is larger than mean) and a high frequency of zero counts. In this study, we used six generalized linear models to examine the relationship between the occurrence of lightning-induced forest fires and meteorological factors in the Northern Daxing'an Mountains of China. The six models included Poisson, negative binomial (NB), zero- inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), Poisson hurdle (PH), and negative binomial hurdle (NBH) models. Goodness-of-fit was compared and tested among the six models using Akaike information criterion (AIC), sum of squared errors, likelihood ratio test, and Vuong test. The predictive performance of the models was assessed and compared using independent validation data by the data-splitting method. Based on the model AIC, the ZINB model best fitted the fire occurrence data, followed by (in order of smaller AIC) NBH, ZIP, NB, PH, and Poisson models. The ZINB model was also best for pre- dicting either zero counts or positive counts (〉1). The two Hurdle models (PH and NBH) were better than ZIP, Poisson, and NB models for predicting positive counts, but worse than these three models for predicting zero counts. Thus, the ZINB model was the first choice for modeling the occurrence of lightning-induced forest fires in this study, which implied that the excessive zero counts of lightning- induced fires came from both structure and sampling zeros.展开更多
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 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Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
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.
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.
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A Poisson regression model and a negative binomial regression model(NB model) are often used in areas such as medicine and economy,but rarely in the domestic forestry sector,especially in the forest fire forecasting.Based on the data of forest fire occurrences in Daxing’anling region in 1980- 2005,this paper profoundly analyzes the application conditions and test methods of the two models.The AIC method was used to check the fitting level of the models and the capability of the models for forecasting forest fires was discussed.This study provided necessary theoretical basis and data support for the application of the two models in the field of forestry in China.
基金funded by Asia–Pacific Forests Net(APFNET/2010/FPF/001)National Natural Science Foundation of China(Grant No.31400552)
文摘The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion (i.e., variance is larger than mean) and a high frequency of zero counts. In this study, we used six generalized linear models to examine the relationship between the occurrence of lightning-induced forest fires and meteorological factors in the Northern Daxing'an Mountains of China. The six models included Poisson, negative binomial (NB), zero- inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), Poisson hurdle (PH), and negative binomial hurdle (NBH) models. Goodness-of-fit was compared and tested among the six models using Akaike information criterion (AIC), sum of squared errors, likelihood ratio test, and Vuong test. The predictive performance of the models was assessed and compared using independent validation data by the data-splitting method. Based on the model AIC, the ZINB model best fitted the fire occurrence data, followed by (in order of smaller AIC) NBH, ZIP, NB, PH, and Poisson models. The ZINB model was also best for pre- dicting either zero counts or positive counts (〉1). The two Hurdle models (PH and NBH) were better than ZIP, Poisson, and NB models for predicting positive counts, but worse than these three models for predicting zero counts. Thus, the ZINB model was the first choice for modeling the occurrence of lightning-induced forest fires in this study, which implied that the excessive zero counts of lightning- induced fires came from both structure and sampling zeros.