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.

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

Binomial model on seismic risk analysis

In this paper, from the differences to evaluate and manage the seismic uncertainty we analyzed the imperfection of determinant method and the Poisson model of probabilistic method in seismic risk analysis. Through studying and summarizing the relation of earthquake occurrence time, intensity and place, we deemed that the time uncertainty of earthquake occurrence interacts with that of space. We expressed the interaction with the concept of upbound earthquake occurrence number and deduced the Binomial model. The Binomial model can be applied in reflecting uncertainty of time and space. Comparing the determinant method and the Poisson model of probabilistic method with the Binomial model, we have got the idea that determinant and the Poisson model are two limits of the Binomial model. When the temporal-spatial uncertainty is infinity or infinitesimal, the binomial model tends to a determinant method and a Poisson model respectively. We also gave an approach to show the implied probability of intensity in the Earthquake intensity Zoning Map in China made in 1977. We also estimated the maximums of the implied probability of five high intensity areas in the Northern China.

Optimal Dividend Strategy in Compound Binomial Model with Bounded Dividend Rates

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.

THE COMPOUND BINOMIAL MODEL WITH A CONSTANT DIVIDEND BARRIER AND PERIODICALLY PAID DIVIDENDS

Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.

Using Binomial Tree Pricing Model in a Fuzzy Market

A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.

Application of Binomial Option Pricing Model to the Appraisal of Knowledge Management Investment

This paper views knowledge management （KM） investment from the angle of real options, and demonstrates the utility of the real options approach to KM investment analysis. First, KM project has characteristics of uncertainty, irreversibility and choice of timing, which suggests that we can appraise KM investment by real options theory. Second, the paper analyses corresponding states of real options in KM and finance options. Then, this paper sheds light on the way to the application of binomial pricing method to KM investment model, which includes modeling and conducting KM options. Finally, different results are shown of using DCF method and binomial model of option evaluation via a case.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

A STATISTICAL MODEL FOR PREDICTION OF INTENSITY AND FREQUENCY OF TROPICAL CYCLONES MAKING LANDFALL ON CHINA

Based on NCEP/NCAR reanalysis data and Yearbook of China landfalling tropical cyclones(hereafter CLTC) from 1949 to 2008,correlation between CLTC frequency/intensity and 500 hPa height field and sea surface temperature(SST) fields are investigated and employed for TC statistical prediction.A prediction model for yearly and monthly intensity and frequency of CLTC is established with binomial curve fitting by choosing the gridpoints with high correlation coefficients as composite factors.Good performance of the model in experiments shows that the model could be used in routine forecast.

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.

The Impacts of Mosquito Density and Meteorological Factors on Dengue Fever Epidemics in Guangzhou, China, 2006-2014: a Time-series Analysis

Objective To explore the associations between the monthly number of dengue fever（DF） cases and possible risk factors in Guangzhou, a subtropical city of China. Methods The monthly number of DF cases, Breteau Index （BI）, and meteorological measures during 2006-2014 recorded in Guangzhou, China, were assessed. A negative binomial regression model was used to evaluate the relationships between BI, meteorological factors, and the monthly number of DF cases. Results A total of 39,697 DF cases were detected in Guangzhou during the study period. DF incidence presented an obvious seasonal pattern, with most cases occurring from June to November. The current month＇s BI, average temperature （Tare）, previous month＇s minimum temperature （Train）, and Tare were positively associated with DF incidence. A threshold of 18.25℃ was found in the relationship between the current month＇s Tmin and DF incidence. Conclusion Mosquito density, Tove, and Tmin play a critical role in DF transmission in Guangzhou. These findings could be useful in the development of a DF early warning system and assist in effective control and prevention strategies in the DF epidemic.

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.

The Gerber-Shiu Discounted Penalty Function for a Compound Binomial Risk Model with By-claims

A recursive formula of the Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims is obtained. In the discount-free case, an explicit formula is given. Utilizing such an explicit expression, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin.

Safety Analysis of Riding at Intersection Entrance Using Video Recognition Technology

To study riding safety at intersection entrance,video recognition technology is used to build vehicle-bicycle conflict models based on the Bayesian method.It is analyzed the relationship among the width of nonmotorized lanes at the entrance lane of the intersection,the vehicle-bicycle soft isolation form of the entrance lane of intersection,the traffic volume of right-turning motor vehicles and straight-going non-motor vehicles,the speed of right-turning motor vehicles,and straight-going non-motor vehicles,and the conflict between right-turning motor vehicles and straight-going nonmotor vehicles.Due to the traditional statistical methods,to overcome the discreteness of vehicle-bicycle conflict data and the differences of influencing factors,the Bayesian random effect Poisson-log-normal model and random effect negative binomial regression model are established.The results show that the random effect Poisson-log-normal model is better than the negative binomial distribution of random effects;The width of non-motorized lanes,the form of vehicle-bicycle soft isolation,the traffic volume of right-turning motor vehicles,and the coefficients of straight traffic volume obey a normal distribution.Among them,the type of vehicle-bicycle soft isolation facilities and the vehicle-bicycle traffic volumes are significantly positively correlated with the number of vehicle-bicycle conflicts.The width of non-motorized lanes is significantly negatively correlated with the number of vehicle-bicycle conflicts.Peak periods and flat periods,the average speed of right-turning motor vehicles,and the average speed of straight-going non-motor vehicles have no significant influence on the number of vehicle-bicycle conflicts.

Some Large Deviation Results for Generalized Compound Binomial Risk Models

This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ > 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.

Option Pricing Method in a Market Involving Interval Number Factors

The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.

Multivariate Analyses for Finding Significant Track Irregularities to Generate an Optimal Track Maintenance Schedule

We first discuss the relationship between the optimal track maintenance scheduling model and an efficient detection method for abnormal track irregularities given by the longitudinal level irregularity displacement (LLID). The results of applying the cluster analysis technique to the sampling data showed that maintenance operation is required for approximately 10% of the total lots, and these lots were further classified into three groups according to the degree of maintenance need. To analyze the background factors for detecting abnormal LLID lots, a principal component analysis was performed;the results showed that the first principal component represents LLIDs from the viewpoints of the rail structure, equipment, and operating conditions. Binomial and ordinal logit regression models (LRMs) were used to quantitatively investigate the determinants of abnormal LLIDs. Binomial LRM was used to characterize the abnormal LLIDs, whereas ordinal LRM was used to distinguish the degree of influence of factors that are considered to have a significant impact on LLIDs.