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.

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.

A spatially-explicit count data regression for modeling the density of forest cockchafer(Melolontha hippocastani) larvae in the Hessian Ried(Germany)

Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are

CONDITIONAL RECURSIVE EQUATIONS ON EXCESS-OF-LOSS REINSURANCE

The rharginal recursive equations on excess-of-loss reinsurance treaty are investignted, under the assumption that the number of claims belongs to the family consisting of Poisson, binomial and negative binomial, and that the severity distribution has bounded continuous density function. On conditional of the numbers of claims associated with the reinsurer and the cedent, some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.

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.

Slow Particle Production in Nucleus-Nucleus Collisions at Relativistic Energies

In this paper an effort has been made to study the general characteristics of slow particles produced in the interactions of 32S-Em at 200 AGeV to extract the information about the mechanism of particle production. The results have been compared with the experimental results obtained by other workers. The multiplicity distributions of the slow target associated particles (black, grey and heavy tracks) produced by 32S-beam with different targets have been studied. Also several types of correlations among them have been investigated. The variation of the produced particles with projectile mass number and target size has been studied. Also the multiplicity distributions of slow particles with NBD fits are presented and scaling multiplicity distributions of slow particles produced have been studied in order to check the validity of KNO-scaling.

Approximation for counts of head runs

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.

Approximation for Counts of 2-runs in a Two State Markov Chain

We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.

The Gamma/Weibull Customer Lifetime Model

This paper proposes a new customer lifetime model:the Gamma/Weibull distribution(G/W).Similar to the Pareto/NBD model,we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution(NBD)and study its properties such as(i)the probability that a customer to be alive at a time point;(ii)the expectation and variance of the number of transactions for a customer during a fixed time period;(iii)the conditional expectation and conditional variance of the number of future transactions for a customer during a fixed time period.Several simulation studies are conducted to investigate the forecasting accuracy and flexibility of the proposed model.A CDNOW data set is analyzed by the proposed model.