Conditional autoregressive negative binomial model for analysis of crash count using Bayesian methods

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.

Evolution law of a negative binomial state in an amplitude dissipative channel

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.

Wigner Function of Density Operator for Negative Binomial Distribution

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.

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

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.

Time evolution of negative binomial optical field in a diffusion channel

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.

Negative Binomial Distribution Based Reputation Direct Update for Wireless Sensor Networks

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.

Zero-inflated non-central negative binomial distribution

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.

Poisson and Negative Binomial Modeling Techniques for Better Understanding Pasteuria penetrans Spore Attachment on Root-Knot Nematode Juveniles

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.

A First Order Stationary Branching Negative Binomial Autoregressive Model with Application

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.

A Hurdle Negative Binomial Regression Model for Non-Marital Fertility in Namibia

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.

Assessing the Robustness of the Negative Binomial Multiple Change Point Algorithm Using Synthetic Data

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.

Advanced Algorithm for Parameters Estimation of Negative Binomial Distribution with High Dimensional Sparse Group Structure

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.

Minimum Density Power Divergence Estimator for Negative Binomial Integer-Valued GARCH Models

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.

Large Deviation Results for Generalized Compound Negative Binomial Risk Models

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.

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

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.

Differential influences of road physical design attributes on pedestrian versus driver traffic accident frequencies

Traffic accidents involving pedestrians and drivers pose significant public health and safety concerns.Understanding the differential influences of road physical design attributes on crash frequencies for these two groups is critical for developing targeted safety interventions.Considering that the zero-truncated characteristic of the data is uncertain,the results of the zero-truncated negative binomial models and traditional negative binomial models are calculated to seek the better model.The result revealed that the road surface conditions and vertical and horizontal curvature have greater influence on both pedestrian and driver compared to number of lanes and speed limit.And speed limits were more pronounced for pedestrian crash frequency than driver group.Conversely,the effect of different types of intersections was stronger for driver crash frequency.The differential influences of road physical design attributes on traffic crash frequencies for pedestrians versus drivers highlight the importance of adopting a user-centric approach to transportation safety planning and infrastructure design.Tailoring interventions to address the unique needs and vulnerabilities of different road user groups can lead to more effective safety improvements and better overall traffic safety outcomes.

Comparison of six generalized linear models for occurrence of lightning-induced fires in northern Daxing'an Mountains,China

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.

Construction of crash prediction model of freeway basic segment based on interactive influence of explanatory variables

In order to improve the prediction precision of the safety performance function （SPF） of freeway basic segments, design and crash data of 640 segments are collected from different institutions. Three negative binomial （NB） regression models and three generalized negative binomial （GNB） regression models are built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The effective use of the GNB model in analyzing the interactive influence of explanatory variables and predicting freeway basic segments is demonstrated. Among six models, the two models （one is the NB model and the other is the GNB model. ） which consider the interactive influence of the annual average daily traffic （AADT） and length are more reasonable for predicting results. Furthermore, a comprehensive study is carried out to prove that when considering the interactive influence, the NB and GNB models have almost the same fitting performance in estimating the crashes, among which the GNB model is slightly better for prediction performance.

AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS

The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables.This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results.Using Trotter-operator technique together with Zolotarev-distance's ideality,some upper bounds of convergence rates of normalized negative binomial random sums(in the sense of convergence in distribution)to Gamma,generalized Laplace and generalized Linnik random variables are established.The obtained results are extension and generalization of several known results related to geometric random sums.

Spatial Evolution and Locational Determinants of High-tech Industries in Beijing

Using datasets on high-tech industries in Beijing as empirical studies, this paper attempts to interpret spatial shift of high-tech manufacturing firms and to examine the main determinants that have had the greatest effect on this spatial evolution. We aimed at merging these two aspects by using firm level databases in 1996 and 2010. To explain spatial change of the high-tech firms in Beijing, the Kernel density estimation method was used for hotspot analysis and detection by comparing their locations in 1996 and 2010, through which spatial features and their temporal changes could be approximately plotted. Furthermore, to provide quantitative results, Ripley′s K-function was used as an instrument to reveal spatial shift and the dispersion distance of high-tech manufacturing firms in Beijing. By employing a negative binominal regression model, we evaluated the main determinants that have significantly affected the spatial evolution of high-tech manufacturing firms and compared differential influence of these locational factors on overall high-tech firms and each sub-sectors. The empirical analysis shows that high-tech industries in Beijing, in general, have evident agglomeration characteristics, and that the hotspot has shifted from the central city to suburban areas. In combination with the Ripley index, this study concludes that high-tech firms are now more scattered in metropolitan areas of Beijing as compared with 1996. The results of regression model indicate that the firms′ locational decisions are significantly influenced by the spatial planning and regulation policies of the municipal government. In addition, market processes involving transportation accessibility and agglomeration economy have been found to be important in explaining the dynamics of locational variation of high-tech manufacturing firms in Beijing. Research into how markets and the government interact to determine the location of high-tech manufacturing production will be helpful for policymakers to enact effective policies toward a more efficient urban spatial structure.